DOCSLIB.ORG

Staff Profile Personal Information

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Staff Profile Personal Information CAUVERY COLLEGE FOR WOMEN (AUTONOMOUS) STAFF PROFILE PERSONAL INFORMATION 1. Name : JANAKI.G 2. Date of Birth : 30.05.1970 3. Address : Residential Office RK Manor, Cauvery College for Women(Autonomous), B2, II Floor, SBO Colony, Annamalai Nagar, Lawson’s Road, Cantonment, Tiruchirappalli-620018 Trichy-620 001 E-Mail: [email protected] Mobile:9443625112 4. PAN Number : AJLPJ3380L 5. Aadhar Card Number : 9431 7125 1406 ACADEMIC INFORMATION 6. Designation & Department: Associate Professor, Department of Mathematics. 7. Educational Qualification : Degree Year College/University Ph.D., 2011 National College, Trichy. M.Phil., 1995 St.Joseph College, Trichy. M.Sc., 1993 Seethalakshmi Ramaswami College, Trichy. B.Sc., 1991 Seethalakshmi Ramaswami College, Trichy. 8. Experience : Date of Joining Institution Year of Experience 28.11.2003 Cauvery College for Women 17 Years 8 Months 9. Areas of Specialization : Number Theory 10. Languages known : Tamil, English 11. Subjects Taught : UG Abstract Algebra, Complex Analysis, Statics, Dynamics, Probability and Statistics, Sequences and Series, Differential Equations and Laplace Transforms, Integral Calculus and Analytical Geometry of 3D, Practical Statistics, Numerical Methods, Operations Research, Number Theory, Algebra and Calculus, Biostatistics, Algebra, Analytical Geometry of 3D and Trigonometry PG Topology, Functional Analysis, Optimization Techniques, Discrete Mathematics, Integral equations, Calculus of Variations and Fourier Transforms, Classical Dynamics, Ordinary Differential Equations, Partial Differential Equations, Algebraic Number Theory 12. Research Supervision: Thesis University from where Completed Year of Pursuing guideship obtained (in numbers) Completion (in numbers) M.Phil Bharathidasan University Ph.D Bharathidasan - - 04 University 13. Details of Publications: Year of ISSN Impact Journal Name & Volume Name of the Paper Publication Number Factor Acta Ciencia Indica, 2007 0970-0455 A Remarkable Pythagorean - XXXIIIM(4) Problem Acta Ciencia Indica, 2008 0970-0455 Observation on - XXXIVM(2) Y 2 3X 2 1 Impact Journal of 2008 0973-8290 Integral solutions of - Science and Technology Ternary Quadratic equation x2 y2 xy z2 Bulletin of Pure and 2008 0970-6577 Pythagorean triangle with - Applied Sciences, Area/Perimeter as a special 27(E)(2) polygonal number Antarctica J. 2008 0972-8643 Pythagorean Triangle with - Math., 5(2) perimeter as Pentogonal number Journal of Applied 2008 0973-3884 Pythagorean Triangle with - Mathematical Analysis Nasty number as a leg and Applications (Serial Publications), (4)1-2 Impact Journal of 2008 0973-8290 Pythagorean Triangle and - Science and Technology, Nasty number 2(1) Impact Journal of 2008 0973-8290 Integral solutions of - Science and Technology, Ternary Quadratic equation 2(2) x 2 y 2 z 2 4 Impact Journal of 2008 0973-8290 Observations on - Science and Tchnology, x2 y2 x y 2(3) xy 2 Impact Journal of 2008 0973-8290 Pythagorean Triangle with - Science and Technology, Pentagonal number as 2(4) Perimeter Cauvery Research July 2008 Observations on - Journal, 2(1) 2(x2 y2 ) 4xy (k 2 4k 4)z3 Impact J.Sci.Tech,, 3(3) 2009 0973-8290 On Pairs of Rectangles - Proceedings of the 2009 ISBN: Integral Solutions of - International Conference 978-81- x2 y2 z2 4 on Mathematical 8424-466- Methods and 3 Computation, Jamal Mohammed College (Autononous), Tiruchirappalli, India Acta Ciencia Indica, 2009 Observation on - 0970-0455 Vol. XXXV M(2) 2(x2 y 2 ) 4xy z 4 2010 0973-8290 Integral Solutions of - Impact J.Sci.Tech.,, 4 (x 2 y 2 )(3x 2 3y 2 2xy) 2(z 2 w2 ) p3 Antarctica J. 2010 0972-8643 Integral Solution of - Math., 7(1) x 2 y 2 xy (m 2 5n 2 )z 3 Antarctica J. 2010 0972-8643 Observations on - Math., 7(2) 3(x2 y2) 9xy z4 Antarctica J. 2010 0972-8643 Integral Solutions of - Math., 7(1) xy x y 1 z2 w2 2010 0972-8643 Integral solutions of - Impact J.Sci.Tech., 4 (x2 y2)(3x2 3y2 2xy) 2(z2 w2) p3 Archimedes - Observations on - 2011 J.Math., 1(2) xy x y 1 kz2 Reflections des ERA, 0973-4597 Pythagorean triangles with - 2011 6(4) Perimeter as a Nasty number Jamal Academic 2011 0973-0303 On the Ternary Quadratic - Research Journal: An Diophantine equation Interdisciplinary, Special 6(x2 y2) 11xy 2(x y) 4 Issue 27z2 International Journal of Engineering Research- Rectangle with Area as a Online, Jan-Feb, special polygonal number 2321-7758 A Peer Reviewed 2016 3.601 International Journal, 4(1) International Journal of Integral Solutions Science and 2016 2319-7064 5.611 of 4w2 x2 y2 z2 t2 Research(IJSR), 5(1) International Journal for Research in Applied Special pairs of rectangles Science and Feb-2016 2321-9653 5.011 and sphenic number Engineering Technology (IJRASET), 4(II) International Journal of Special Pythagorean Innovative Research in March 2319-8753 triangles and 6-digit 5.442 Science, Engineering 2016. Harshad numbers and Technology, 5(2) Jamal Academic Pythagorean triangle with Research Journal: An February - 0973-0303 Heptagonal number as Interdisciplinary Special 2016 Perimeter Issue Observations On Ternary Jamal Academic Quadratic Equation - Research Journal: An February 0973-0303 5x2 7y2 972z2 Interdisciplinary Special 2016 Issue American International December, Special pairs of Journal of Research in 2015- 2328-3491 Pythagorean Triangles and Science, Technology, 5.01 Febuary, Jarasandha Engineering and 2016 Numbers Mathematics, 13(2) International Journal of On the Ternary Quadratic 2454-1362 3.75 Interdisciplinary 2016 Diophantine Equation Research(IJIR), 2(3) 5(x2 y2 ) 6xy 4z 2 Observations on Ternary International Journal Quadratic Diophantine of Innovative Research 2347-6710 February Equation 5.442 in Science, Engineering 2016 6(x2 y2 ) 11xy 3x 3y 9 72z2 and Technology,5(2) International Journal for Research in Applied Special pairs of Rectangle February- Science 2321-9653 and Sphenic 5.011 2016 and Engineering number Technology, 4(2) International Journal of Connection between 2349-4182 Multidisciplinary special Pythagorean March 2016 5.72 Research and triangles and Jarasandha Development, 3(3) numbers International Journal of On the Ternary Cubic Science and Research March 2016 Diophantine Equation 5.611 (IJSR), 5(3) 2319-7064 5(x2 y2) 6xy 4(x y) 4 40z3 Bulletin of Mathematics and Statistics Research(A April-June, 2348-0580 Special Rectangles and 4.495 Peer Reviewed 2016 Jarasandha Numbers International Research Journal), 4(2) International Journal of 2349-4182 Special pairs of Multidisciplinary April 2016 Pythagorean triangles and 5.72 Research Narcissistic number and Development, 3(4) International Journal of On the integer solutions of Science, Engineering 2394-4099 April 2016 the pell equation 3.7 and x2 79 y2 9k Technology, 2(2) International Journal of On the integer solutions of Multidisciplinary 2349-4182 May 2016 the pell equation 5.72 Research and x2 20 y2 4t Development, 3(5) Asian Journal of 0976-3376 Special pairs of Rectangles 5.544 Science and Technology, May 2016 and Jarasandha numbers 7(5) Integral solutions of the non-homogeneous heptic equation with five International Journal of unknowns 2321-3361 Engineering, Science 3 3 2 2 5.611 May-2016 5(x y ) 7(x y ) and Computing, 6(5) 4(z3 w3 3wz xy 1) 972 p7 On the integer solutions of International Journal of 2321-3361 the homogeneous bi- Engineering, Science 5.611 June-2016 quadratic Diophantine and Computing, 6(6) equation x4 y4 82(z 2 w2 ) p2 American International Journal of Research in Special pairs Pythagorean June- 2328-3580 Science, Technology, triangles and 2-digits 5.01 August- Engineering and sphenic numbers 2016 Mathematics, 15(1) International Research Pythagorean Triangle with 2395-0056 Journal of Engineering Area/Perimeter as a 4.45 July-2016 and Technology, 3(7) Jarasandha Number of order 2 &4 American International Journal of Research in Special Pythagorean Science, Technology, March- 2328-3580 Triangles in Connection 5.01 Engineering and May, 2016 with the Narcissistic Mathematics, Volume 2, Numbers of Order 3 and 4 Issue14, International Journal of Engineering Science and Observations on May 2016 2321-3361 computing, Volume 6, “ x224 xy y 22 x 0 ” 5.611 Issue 5 International Journal For Research in Applied Special Rectangles and 2321-9653 Science and Engineering June 2016 Narcissistic Numbers of 5.011 Technology, Volume 4, Order 3 and 4 Issue VI Universal Journal of Observations on Truncated Mathematics, Volume 3, June 2016 2456-1312 - Octahedral Number Issue 3 International Research Special pairs of rectangles Journal of Engineering August 2395-0056 and Narcissistic numbers of 4.45 and Technology, 2016 order 3 and 4 Volume 3, Issue 8 Asian Journal of Science Special pairs of August and Technology , 0976-3376 Pythagorean triangles and 2016 6.351 Volume 7, Issue 8 Harshad numbers International Journal of Nov 2016 2394-5869 On the negative Pell 5.2 Applied Research, equation y2 = 21x2 – 3 Volume 2, Issue 11 International Journal of Nov 2016 2455-4197 Special pairs of 5.22 Academic Research and Pythagorean triangles and Development, Volume 1, 3-digit consecutive sphenic Issue 11 numbers International Journal of Jan 2017 2455-4030 Construction of Special 5.24 Advanced Research and Dio 3-Tuples from Development(ijard), CCn Volume 2, Issue 6 I Gnon International Journal of On the Quinitic Non- Engineering Science and February 2321-3361 Homogeneous Diophantine 5.611 Computing, Volume 7, 2017 Equation Issue 2 x4 y4 40(z2 w2)p3 International Research Integral solutions
Load more

Recommended publications
  • Guidance Via Number 40: a Unique Stance M
    Sci.Int.(Lahore),31(4),603-605, 2019 ISSN 1013-5316;CODEN: SINTE 8 603 GUIDANCE VIA NUMBER 40: A UNIQUE STANCE M. AZRAM 7-William St. Wattle Grove, WA 6107, USA. E-mail: [email protected] ABSTRACT: The number Forty (40) is a mysterious number that has a great significance in Mathematics, Science, astronomy, sports, spiritual traditions and many cultures. Historically, many things took place labelled with number 40. It has also been repeated many times in Islam. There must be some significantly importance associated with this magic number 40. Only Allah knows the complete answer. Since Muslims are enjoined to establish good governance through a just sociomoral order (or a state) wherein they could organise their individual and collective life in accordance with the teachings of the Qur’an and the Sunnah of the Prophet (SAW). I have gathered together some information to find some guideline via significant number 40 to reform our community by eradicating corruption, exploitation, injustice and evil etc. INTRODUCTION Muslims are enjoined to establish good governance through a just sociomoral order (or a state) wherein they could organise their individual and collective life in accordance with the teachings of the Qur’an and the Sunnah of the pentagonal pyramidal number[3] and semiperfect[4] .It is the expectation of the Qur’an that its number which have fascinated mathematics .(ﷺ) Prophet 3. 40 is a repdigit in base 3 (1111, i.e. 30 + 31 + 32 + 33) adherents would either reform the earth (by eradicating , Harshad number in base10 [5] and Stormer number[6]. corruption, exploitation, injustice and evil) or lay their lives 4.
    [Show full text]
  • Monthly Science and Maths Magazine 01
    1 GYAN BHARATI SCHOOL QUEST….. Monthly Science and Mathematics magazine Edition: DECEMBER,2019 COMPILED BY DR. KIRAN VARSHA AND MR. SUDHIR SAXENA 2 IDENTIFY THE SCIENTIST She was an English chemist and X-ray crystallographer who made contributions to the understanding of the molecular structures of DNA , RNA, viruses, coal, and graphite. She was never nominated for a Nobel Prize. Her work was a crucial part in the discovery of DNA, for which Francis Crick, James Watson, and Maurice Wilkins were awarded a Nobel Prize in 1962. She died in 1958, and during her lifetime the DNA structure was not considered as fully proven. It took Wilkins and his colleagues about seven years to collect enough data to prove and refine the proposed DNA structure. RIDDLE TIME You measure my life in hours and I serve you by expiring. I’m quick when I’m thin and slow when I’m fat. The wind is my enemy. Hard riddles want to trip you up, and this one works by hitting you with details from every angle. The big hint comes at the end with the wind. What does wind threaten most? I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I? This riddle aims to confuse you and get you to focus on the things that are missing: the houses, trees, and fish. 3 WHY ARE AEROPLANES USUALLY WHITE? The Aeroplanes might be having different logos and decorations. But the colour of the aeroplane is usually white.Painting the aeroplane white is most practical and economical.
    [Show full text]
  • Correspondent Speaks
    CORRESPONDENT SPEAKS In today’s changing scenario, there is an increasing necessity of empowering the students through innovative education. They should also be made aware of their rights and responsibilities. In the present system, students gain mere subject knowledge through the educational institutions. A healthy educational environment will cultivate positive personality among the students. “Students of today are the citizens of tomorrow” and so, they should be motivated towards the right direction. This magazine encompassing Puzzles, Aptitude questions, Vedic Maths and many more will create flourishing impact in the mind of the readers. I wish all the budding mathematics genius, a good luck. FROM THE PRINCIPAL’ S DESK Creativity keeps the human being on the path of progress and helps for perpetuity and comfort. Innovative thoughts make global changes. This magazine is a testimony to the creative skills of our students. Roll of honour and the achievements of the department are milestones of the department. The articles of the creators embellish this magazine. Wish them all a great success. HEAD OF THE DEPARTMENT’S MESSAGE Warm Greetings . I would like to express my gratitude to the patron Thiru P.Sachithanandan, Correspondent, KASC, the editorial board of this MATHEZINE and all the contributors. Sit back, relax and have sweet memories of the year passed. I feel proud to get published in this magazine, our successful activities and events of the academic year 2013-14. With hope and confidence in the family of mathemat ics at Kongu Arts and Science College, which is marching towards progress and prosperity, I pray to the almighty for a healthy, wealthy and pr osperous life to all my students.
    [Show full text]
  • Large and Small Gaps Between Consecutive Niven Numbers
    1 2 Journal of Integer Sequences, Vol. 6 (2003), 3 Article 03.2.5 47 6 23 11 Large and small gaps between consecutive Niven numbers Jean-Marie De Koninck1 and Nicolas Doyon D¶epartement de math¶ematiques et de statistique Universit¶e Laval Qu¶ebec G1K 7P4 Canada [email protected] [email protected] Abstract A positive integer is said to be a Niven number if it is divisible by the sum of its decimal digits. We investigate the occurrence of large and small gaps between consecutive Niven numbers. 1 Introduction A positive integer n is said to be a Niven number (or a Harshad number) if it is divisible by the sum of its (decimal) digits. For instance, 153 is a Niven number since 9 divides 153, while 154 is not. Niven numbers have been extensively studied; see for instance Cai [1], Cooper and Kennedy [2], Grundman [5] or Vardi [6]. Let N(x) denote the number of Niven numbers · x. Recently, De Koninck and Doyon proved [3], using elementary methods, that given any " > 0, x log log x x1¡" ¿ N(x) ¿ : log x Later, using complex variables as well as probabilistic number theory, De Koninck, Doyon and K¶atai [4] showed that x N(x) = (c + o(1)) ; (1) log x 1Research supported in part by a grant from NSERC. 1 where c is given by 14 c = log 10 ¼ 1:1939: (2) 27 In this paper, we investigate the occurrence of large gaps between consecutive Niven numbers. Secondly, denoting by T (x) the number of Niven numbers n · x such that n + 1 is also a Niven number, we prove that x log log x T (x) ¿ : (log x)2 We conclude by stating a conjecture.
    [Show full text]
  • ~Umbers the BOO K O F Umbers
    TH E BOOK OF ~umbers THE BOO K o F umbers John H. Conway • Richard K. Guy c COPERNICUS AN IMPRINT OF SPRINGER-VERLAG © 1996 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1996 All rights reserved. No part of this publication may be reproduced, stored in a re­ trieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Published in the United States by Copernicus, an imprint of Springer-Verlag New York, Inc. Copernicus Springer-Verlag New York, Inc. 175 Fifth Avenue New York, NY lOOlO Library of Congress Cataloging in Publication Data Conway, John Horton. The book of numbers / John Horton Conway, Richard K. Guy. p. cm. Includes bibliographical references and index. ISBN-13: 978-1-4612-8488-8 e-ISBN-13: 978-1-4612-4072-3 DOl: 10.l007/978-1-4612-4072-3 1. Number theory-Popular works. I. Guy, Richard K. II. Title. QA241.C6897 1995 512'.7-dc20 95-32588 Manufactured in the United States of America. Printed on acid-free paper. 9 8 765 4 Preface he Book ofNumbers seems an obvious choice for our title, since T its undoubted success can be followed by Deuteronomy,Joshua, and so on; indeed the only risk is that there may be a demand for the earlier books in the series. More seriously, our aim is to bring to the inquisitive reader without particular mathematical background an ex­ planation of the multitudinous ways in which the word "number" is used.
    [Show full text]
  • Special Pythagorean Triangle in Relation with Pronic Numbers
    International Journal of Mathematics Trends and Technology (IJMTT) – Volume 65 Issue 8 - August 2019 Special Pythagorean Triangle In Relation With Pronic Numbers S. Vidhyalakshmi1, T. Mahalakshmi2, M.A. Gopalan3 1,2,3(Department of Mathematics, Shrimati Indra Gandhi College, India) Abstract: 2* Area This paper illustrates Pythagorean triangles, where, in each Pythagorean triangle, the ratio Perimeter is a Pronic number. Keywords: Pythagorean triangles,Primitive Pythagorean triangle, Non primitive Pythagorean triangle, Pronic numbers. Introduction: It is well known that there is a one-to-one correspondence between the polygonal numbers and the sides of polygon. In addition to polygon numbers, there are other patterns of numbers namely Nasty numbers, Harshad numbers, Dhuruva numbers, Sphenic numbers, Jarasandha numbers, Armstrong numbers and so on. In particular, refer [1-17] for Pythagorean triangles in connection with each of the above special number patterns. The above results motivated us for searching Pythagorean triangles in connection with a new number pattern. This paper 2* Area illustrates Pythagorean triangles, where, in each Pythagorean triangle, the ratio is a Pronic number. Perimeter Method of Analysis: Let Tx, y, z be a Pythagorean triangle, where x 2pq , y p2 q2 , z p2 q2 , p q 0 (1) Denote the area and perimeter of Tx, y, z by A and P respectively. The mathematical statement of the problem is 2A nn 1 , pronic number of rank n (2) P qp q nn 1 (3) It is observed that (3) is satisfied by the following two sets of values of p and q: Set 1: p 2n 1, q n Set 2: p 2n 1, q n 1 However, there are other choices for p and q that satisfy (3).
    [Show full text]
  • Generalized Sum of Stella Octangula Numbers
    DOI: 10.5281/zenodo.4662348 Generalized Sum of Stella Octangula Numbers Amelia Carolina Sparavigna Department of Applied Science and Technology, Politecnico di Torino A generalized sum is an operation that combines two elements to obtain another element, generalizing the ordinary addition. Here we discuss that concerning the Stella Octangula Numbers. We will also show that the sequence of these numbers, OEIS A007588, is linked to sequences OEIS A033431, OEIS A002378 (oblong or pronic numbers) and OEIS A003154 (star numbers). The Cardano formula is also discussed. In fact, the sequence of the positive integers can be obtained by means of Cardano formula from the sequence of Stella Octangula numbers. Keywords: Groupoid Representations, Integer Sequences, Binary Operators, Generalized Sums, OEIS, On-Line Encyclopedia of Integer Sequences, Cardano formula. Torino, 5 April 2021. A generalized sum is a binary operation that combines two elements to obtain another element. In particular, this operation acts on a set in a manner that its two domains and its codomain are the same set. Some generalized sums have been previously proposed proposed for different sets of numbers (Fibonacci, Mersenne, Fermat, q-numbers, repunits and others). The approach was inspired by the generalized sums used for entropy [1,2]. The analyses of sequences of integers and q-numbers have been collected in [3]. Let us repeat here just one of these generalized sums, that concerning the Mersenne n numbers [4]. These numbers are given by: M n=2 −1 . The generalized sum is: M m⊕M n=M m+n=M m+M n+M m M n In particular: M n⊕M 1=M n +1=M n+M 1+ M n M 1 1 DOI: 10.5281/zenodo.4662348 The generalized sum is the binary operation which is using two Mersenne numbers to have another Mersenne number.
    [Show full text]
  • Digits Harshad Number *1 2 3 S
    ISSN: 2277-9655 [Mohamed* et al., 6(8): August, 2017] Impact Factor: 4.116 IC™ Value: 3.00 CODEN: IJESS7 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY SPECIAL PAIRS OF PYTHAGOREAN TRIANGLES AND 3 –DIGITS HARSHAD NUMBER *1 2 3 S. Yahya Mohamed , S. Prem Kumar and V. Somu *1 PG & Research Derpartment of Mathematics, Govt. Arts College, Trichy-22. 2M.Phil. Research Scholar, Govt. Arts College, Trichy-22 & 3BT Assisstant, Ayyanar Corporation High School, Srirangam. DOI: 10.5281/zenodo.843869 ABSTRACT Here, we present pairs of Pythagorean triangles such that in each pair, the difference between their perimeters is four times the 3-digit Harshad number 108. Also we present the number of pairs of primitive and non- primitive Pythagorean triangles. KEYWORDS: Pairs of Pythagorean Triangle, Harshad number, Prime numbers. I. INTRODUCTION Number theory is broad and diverse part of Mathematics that developed from the study of the integers. Mathematics all over the ages have been fascinated by Pythagorean Theorem and problem related to it there by developing Mathematics. Pythagorean triangle which first studied by the Pythagorean around 400 B.C., remains one of the fascinated topics for those who just adore the number. In this communication, we search for pairs of Pythagorean triangles, such that in each pair, the difference between their perimeters is 4 times the 3digit Harshad number 108. II. BASIC DEFINITIONS Definition 2.1 2 2 2 The ternary quadric Diophantine equation given by x y z is known as Pythagorean equation where x, y, z are natural numbers. The above equation is also referred to as Pythagorean triangle and denote it by T(x ,y, z).
    [Show full text]
  • Some Links of Balancing and Cobalancing Numbers with Pell and Associated Pell Numbers
    Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 6 (2011), No. 1, pp. 41-72 SOME LINKS OF BALANCING AND COBALANCING NUMBERS WITH PELL AND ASSOCIATED PELL NUMBERS G. K. PANDA1,a AND PRASANTA KUMAR RAY2,b 1 National Institute of Technology, Rourkela -769 008, Orissa, India. a E-mail: gkpanda nit@rediffmail.com 2 College of Arts Science and Technology, Bandomunda, Rourkela -770 032, Orissa, India. b E-mail: [email protected] Abstract Links of balancing and cobalancing numbers with Pell and associated Pell numbers th th are established. It is proved that the n balancing number is product of the n Pell th number and the n associated Pell number. It is further observed that the sequences of balancing and cobalancing numbers are very closely related to the Pell sequence whereas, the sequences of Lucas-balancing and Lucas-cobalancing numbers constitute the associated Pell sequence. The solutions of some Diophantine equations including Pythagorean and Pythagorean-type equations are obtained in terms of these numbers. 1. Introduction The study of number sequences has been a source of attraction to the mathematicians since ancient times. From that time many mathematicians have been focusing their attention on the study of the fascinating triangu- lar numbers (numbers of the form n(n + 1)/2 where n Z+ are known as ∈ triangular numbers). Behera and Panda [1], while studying the Diophan- tine equation 1 + 2 + + (n 1) = (n + 1) + (n +2)+ + (n + r) on · · · − · · · triangular numbers, obtained an interesting relation of the numbers n in Received April 28, 2009 and in revised form September 25, 2009.
    [Show full text]
  • Pra C Tice Ques Tions
    Factors and Multiples 2.9 TEST Your CONCEPTS Very Short Answer Type Questions Direction for questions from 1 to 5: Fill in the Direction for questions from 12 to 16: Fill in the blanks. blanks. 1. The number of factors of 24 is ______. 12. The number of common multiples of 6 and 15 is _____. 2. The greatest 2-digit multiple of 8 is _____. 13. The least common multiple of two co-primes is 3. The greatest common factor of 9 and 15 is _____. _____. 4. The number of prime factors of 48 is ______. 14. LCM (a, b) × HCF (a, b) = _____. 5. The greatest pair of twin primes of 2-digit 15. The largest 3-digit number divisible by 9 is _____. numbers is _____. 16. The smallest 4-digit number divisible by 11 is Direction for questions from 6 to 10: Select the _____. correct alternative from the given choices. Direction for questions from 17 to 22: Select the 6. Which of the following is a prime number? correct alternative from given choices. (a) 87 (b) 69 (c) 57 (d) 97 17. The LCM of a and b is 220. Which of the follow- 7. Which of the following is not a sphenic number? ing can be the HCF of a and b? (a) 30 (b) 42 (c) 60 (d) 70 (a) 33 (b) 15 (c) 20 (d) 12 8. Which of the following is a composite number? 18. Which of the following pairs of numbers have (a) 37 (b) 47 (c) 57 (d) 67 their LCM 144? 9.
    [Show full text]
  • Integer Sequences
    UHX6PF65ITVK Book > Integer sequences Integer sequences Filesize: 5.04 MB Reviews A very wonderful book with lucid and perfect answers. It is probably the most incredible book i have study. Its been designed in an exceptionally simple way and is particularly just after i finished reading through this publication by which in fact transformed me, alter the way in my opinion. (Macey Schneider) DISCLAIMER | DMCA 4VUBA9SJ1UP6 PDF > Integer sequences INTEGER SEQUENCES Reference Series Books LLC Dez 2011, 2011. Taschenbuch. Book Condition: Neu. 247x192x7 mm. This item is printed on demand - Print on Demand Neuware - Source: Wikipedia. Pages: 141. Chapters: Prime number, Factorial, Binomial coeicient, Perfect number, Carmichael number, Integer sequence, Mersenne prime, Bernoulli number, Euler numbers, Fermat number, Square-free integer, Amicable number, Stirling number, Partition, Lah number, Super-Poulet number, Arithmetic progression, Derangement, Composite number, On-Line Encyclopedia of Integer Sequences, Catalan number, Pell number, Power of two, Sylvester's sequence, Regular number, Polite number, Ménage problem, Greedy algorithm for Egyptian fractions, Practical number, Bell number, Dedekind number, Hofstadter sequence, Beatty sequence, Hyperperfect number, Elliptic divisibility sequence, Powerful number, Znám's problem, Eulerian number, Singly and doubly even, Highly composite number, Strict weak ordering, Calkin Wilf tree, Lucas sequence, Padovan sequence, Triangular number, Squared triangular number, Figurate number, Cube, Square triangular
    [Show full text]
  • Fermat Pseudoprimes
    1 TWO HUNDRED CONJECTURES AND ONE HUNDRED AND FIFTY OPEN PROBLEMS ON FERMAT PSEUDOPRIMES (COLLECTED PAPERS) Education Publishing 2013 Copyright 2013 by Marius Coman Education Publishing 1313 Chesapeake Avenue Columbus, Ohio 43212 USA Tel. (614) 485-0721 Peer-Reviewers: Dr. A. A. Salama, Faculty of Science, Port Said University, Egypt. Said Broumi, Univ. of Hassan II Mohammedia, Casablanca, Morocco. Pabitra Kumar Maji, Math Department, K. N. University, WB, India. S. A. Albolwi, King Abdulaziz Univ., Jeddah, Saudi Arabia. Mohamed Eisa, Dept. of Computer Science, Port Said Univ., Egypt. EAN: 9781599732572 ISBN: 978-1-59973-257-2 1 INTRODUCTION Prime numbers have always fascinated mankind. For mathematicians, they are a kind of “black sheep” of the family of integers by their constant refusal to let themselves to be disciplined, ordered and understood. However, we have at hand a powerful tool, insufficiently investigated yet, which can help us in understanding them: Fermat pseudoprimes. It was a night of Easter, many years ago, when I rediscovered Fermat’s "little" theorem. Excited, I found the first few Fermat absolute pseudoprimes (561, 1105, 1729, 2465, 2821, 6601, 8911…) before I found out that these numbers are already known. Since then, the passion for study these numbers constantly accompanied me. Exceptions to the above mentioned theorem, Fermat pseudoprimes seem to be more malleable than prime numbers, more willing to let themselves to be ordered than them, and their depth study will shed light on many properties of the primes, because it seems natural to look for the rule studying it’s exceptions, as a virologist search for a cure for a virus studying the organisms that have immunity to the virus.
    [Show full text]