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file:///Users/raxtus/Dropbox (Personal)/misc/cards.html 1 + 1 157 × 2 Capacity of 26-100 according to 5 + 5 classrooms.mit.edu eπ A googolplex 1 of 5 11/2/18, 2:13 PM file:///Users/raxtus/Dropbox (Personal)/misc/cards.html MIT course number of the Nominal GDP per capita political science of Russia in 2017 (USD) department Number of characters in Number of achievable Richard III that are dead states of a 2×2×2 Rubik's by the end of the play, cube including characters that appear only as ghosts Number of citations on Number of distinct the most cited paper ever Pokémon, as of Gen VII 2 of 5 11/2/18, 2:13 PM file:///Users/raxtus/Dropbox (Personal)/misc/cards.html Number of kernels in a Number of Heinz pickle bag of microwave varieties popcorn (according to Google instant answers) Number of picometers in Population of New a Planck length Hampshire Smallest number ever Price of 1 troy ounce of mentioned in a previous gold in U.S. dollars in 1956 BRAIN WORLD CUP 3 of 5 11/2/18, 2:13 PM file:///Users/raxtus/Dropbox (Personal)/misc/cards.html The expected number of rounds needed in the following process: The 1000th digit of e 48 fair dice are tossed, and all dice showing a deuce is (including the 2) removed. This process is repeated until all dice are removed. The fourth three-digit narcissistic number (a narcissistic number is a number The largest number that that is the sum of its own digits can be represented by each raised to the power of the number of digits; there are four the product of the digits narcissistic numbers with three on a single Splendor card digits, the first three of which are 153, 371, and 407) The number of confirmed The month during which exoplanets discovered by this BRAIN WORLD CUP is the Kepler mission, as of held (as an integer from 1 Thursday, November 1, to 12) 2018 4 of 5 11/2/18, 2:13 PM file:///Users/raxtus/Dropbox (Personal)/misc/cards.html The number X such that X The Ramsey number degrees Fahrenheit R(3, 3) equals X degrees Kelvin The value of the Google The second smallest Sheets expression perfect number DATEVALUE("2018-11-2") Given a 102 × 102 sheet of graph paper and a connected figure of unknown shape consisting of The year of the peace of 101 squares, the smallest Westphalia number of copies of the figure which can be cut out of the square, assuming cutting is done optimally 5 of 5 11/2/18, 2:13 PM.

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4 VI June 2016
4 VI June 2016 www.ijraset.com Volume 4 Issue VI, June 2016 IC Value: 13.98 ISSN: 2321-9653 International Journal for Research in Applied Science & Engineering Technology (IJRASET) Special Rectangles and Narcissistic Numbers of Order 3 And 4 G.Janaki1, P.Saranya2 1,2Department of Mathematics, Cauvery College for women, Trichy-620018 Abstract— We search for infinitely many rectangles such that x2 y2 3A S 2 k2 SK Narcissistic numbers of order 3 and 4 respectively, in which x, y represents the length and breadth of the rectangle. Also the total number of rectangles satisfying the relation under consideration as well as primitive and non-primitive rectangles are also present. Keywords—Rectangle, Narcissistic numbers of order 3 and 4, primitive,non-primitive. I. INTRODUCTION The older term for number theory is arithmetic, which was superseded as number theory by early twentieth century. The first historical find of an arithmetical nature is a fragment of a table, the broken clay tablet containing a list of Pythagorean triples. Since then the finding continues. For more ideas and interesting facts one can refer [1].In [2] one can get ideas on pairs of rectangles dealing with non-zero integral pairs representing the length and breadth of rectangle. [3,4] has been studied for knowledge on rectangles in connection with perfect squares , Niven numbers and kepriker triples.[5-10] was referred for connections between Special rectangles and polygonal numbers, jarasandha numbers and dhuruva numbers Recently in [11,12] special pythagorean triangles in connections with Narcissistic numbers are obtained. In this communication, we search for infinitely many rectangles such that x2 y2 3A S 2 k2 SK Narcissistic numbers of order 3 and 4 respectively, in which x,y represents the length and breadth of the rectangle.
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Maths Secrets of Simpsons Revealed in New Book
MONDAY 7 OCTOBER 2013 WWW.THEDAY.CO.UK Maths secrets of Simpsons revealed in new book The most successful TV show of all time is written by a team of brilliant ‘mathletes’, says writer Simon Singh, and full of obscure mathematical jokes. Can numbers really be all that funny? MATHEMATICS Nerd hero: The smartest girl in Springfield was created by a team of maths wizards. he world’s most popular cartoon a perfect number, a narcissistic number insist that their love of maths contrib- family has a secret: their lines are and a Mersenne Prime. utes directly to the more obvious humour written by a team of expert mathema- Another of these maths jokes – a black- that has made the show such a hit. Turn- Tticians – former ‘mathletes’ who are board showing 398712 + 436512 = 447212 ing intuitions about comedy into concrete as happy solving differential equa- – sent shivers down Simon Singh’s spine. jokes is like wrestling mathematical tions as crafting jokes. ‘I was so shocked,’ he writes, ‘I almost hunches into proofs and formulas. Comedy Now, science writer Simon Singh has snapped my slide rule.’ The numbers are and maths, says Cohen, are both explora- revealed The Simpsons’ secret math- a fake exception to a famous mathemati- tions into the unknown. ematical formula in a new book*. He cal rule known as Fermat’s Last Theorem. combed through hundreds of episodes One episode from 1990 features a Mathletes and trawled obscure internet forums to teacher making a maths joke to a class of Can maths really be funny? There are many discover that behind the show’s comic brilliant students in which Bart Simpson who will think comparing jokes to equa- exterior lies a hidden core of advanced has been accidentally included.
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On Hardy's Apology Numbers
ON HARDY’S APOLOGY NUMBERS HENK KOPPELAAR AND PEYMAN NASEHPOUR Abstract. Twelve well known ‘Recreational’ numbers are generalized and classified in three generalized types Hardy, Dudeney, and Wells. A novel proof method to limit the search for the numbers is exemplified for each of the types. Combinatorial operators are defined to ease programming the search. 0. Introduction “Recreational Mathematics” is a broad term that covers many different areas including games, puzzles, magic, art, and more [31]. Some may have the impres- sion that topics discussed in recreational mathematics in general and recreational number theory, in particular, are only for entertainment and may not have an ap- plication in mathematics, engineering, or science. As for the mathematics, even the simplest operation in this paper, i.e. the sum of digits function, has application outside number theory in the domain of combinatorics [13, 26, 27, 28, 34] and in a seemingly unrelated mathematical knowledge domain: topology [21, 23, 15]. Pa- pers about generalizations of the sum of digits function are discussed by Stolarsky [38]. It also is a surprise to see that another topic of this paper, i.e. Armstrong numbers, has applications in “data security” [16]. In number theory, functions are usually non-continuous. This inhibits solving equations, for instance, by application of the contraction mapping principle because the latter is normally for continuous functions. Based on this argument, questions about solving number-theoretic equations ramify to the following: (1) Are there any solutions to an equation? (2) If there are any solutions to an equation, then are finitely many solutions? (3) Can all solutions be found in theory? (4) Can one in practice compute a full list of solutions? arXiv:2008.08187v1 [math.NT] 18 Aug 2020 The main purpose of this paper is to investigate these constructive (or algorith- mic) problems by the fixed points of some special functions of the form f : N N.
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Single Digits
...................................single digits ...................................single digits In Praise of Small Numbers MARC CHAMBERLAND Princeton University Press Princeton & Oxford Copyright c 2015 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved The second epigraph by Paul McCartney on page 111 is taken from The Beatles and is reproduced with permission of Curtis Brown Group Ltd., London on behalf of The Beneﬁciaries of the Estate of Hunter Davies. Copyright c Hunter Davies 2009. The epigraph on page 170 is taken from Harry Potter and the Half Blood Prince:Copyrightc J.K. Rowling 2005 The epigraphs on page 205 are reprinted wiht the permission of the Free Press, a Division of Simon & Schuster, Inc., from Born on a Blue Day: Inside the Extraordinary Mind of an Austistic Savant by Daniel Tammet. Copyright c 2006 by Daniel Tammet. Originally published in Great Britain in 2006 by Hodder & Stoughton. All rights reserved. Library of Congress Cataloging-in-Publication Data Chamberland, Marc, 1964– Single digits : in praise of small numbers / Marc Chamberland. pages cm Includes bibliographical references and index. ISBN 978-0-691-16114-3 (hardcover : alk. paper) 1. Mathematical analysis. 2. Sequences (Mathematics) 3. Combinatorial analysis. 4. Mathematics–Miscellanea. I. Title. QA300.C4412 2015 510—dc23 2014047680 British Library
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Number Gossip About 10 Years Ago and at first I Uploaded It on My Personal Website [6]
Number Gossip Tanya Khovanova Department of Mathematics, MIT April 15, 2008 Abstract This article covers my talk at the Gathering for Gardner 2008, with some additions. 1 Introduction My pet project Number Gossip has its own website: http://www.numbergossip.com/, where you can plug in your favorite integer up to 9,999 and learn its properties. A behind-the-scenes program checks your number for 49 regular properties and also checks a database for unique properties I collected. 2 Eight The favorite number of this year’s Gathering is composite, deficient, even, odious, palindromic, powerful, practical and Ulam. It is also very cool as it has the rare properties of being a cake and a narcissistic number, as well as a cube and a Fibonacci number. And it also is a power of two. In addition, eight has the following unique properties: • 8 is the only composite cube in the Fibonacci sequence • 8 is the dimension of the octonions and is the highest possible dimension of a normed division algebra • 8 is the smallest number (except 1) which is equal to the sum of the digits of its cube 3 Properties There are 49 regular properties that I check for: arXiv:0804.2277v1 [math.CO] 14 Apr 2008 abundant evil odious Smith amicable factorial palindrome sociable apocalyptic power Fibonacci palindromic prime square aspiring Google pentagonal square-free automorphic happy perfect tetrahedral cake hungry power of 2 triangular Carmichael lazy caterer powerful twin Catalan lucky practical Ulam composite Mersenne prime undulating compositorial Mersenne prime primorial untouchable cube narcissistic pronic vampire deficient odd repunit weird even 1 I selected regular properties for their importance as well as their funny names, so your favorite number could be lucky and happy at the same time, as is the case for 7.
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INDEX to ANSWERS Issue Page Number Symmetryplus 60 2
INDEX TO ANSWERS Issue Page number SYMmetryplus 60 2 SYMmetryplus 61 4 SYMmetryplus 62 5 SYMmetryplus 63 8 SYMmetryplus 64 9 SYMmetryplus 65 10 SYMmetryplus 66 13 SYMmetryplus 67 15 SYMmetryplus 68 17 SYMmetryplus 69 21 SYMmetryplus 70 25 SYMmetryplus 71 29 SYMmetryplus 72 33 SYMmetryplus 73 37 SYMmetryplus 74 44 1 ANSWERS FROM ISSUE 60 SOME TRIANGLE NUMBERS – 2 Many thanks to Andrew Palfreyman who found five, not four solutions! 7 7 7 7 7 1 0 5 3 0 0 4 0 6 9 0 3 9 4 6 3 3 3 3 1 Grid A 6 6 1 3 2 6 2 0 1 6 0 0 Grid B CROSSNUMBER Many thanks again to Andrew Palfreyman who pointed out that 1 Down and 8 Across do not give unique answers so there are four possible solutions. 1 2 1 2 1 2 1 2 1 4 4 8 1 4 4 8 1 4 4 8 1 4 4 8 3 3 3 3 3 9 1 9 8 9 1 9 3 9 1 9 8 9 1 9 4 5 4 5 4 5 4 5 2 3 1 0 2 3 1 0 2 3 1 0 2 3 1 0 6 7 6 7 6 7 6 7 1 0 9 8 1 0 9 8 1 0 9 8 1 0 9 8 8 9 8 9 8 9 8 9 3 6 1 0 3 6 1 0 9 6 1 0 9 6 1 0 10 10 10 10 5 3 4 3 5 3 4 3 5 3 4 3 5 3 4 3 TREASURE HUNTS 12, 13 12 This is a rostral column in St Petersburg, Russia.
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Various Arithmetic Functions and Their Applications
University of New Mexico UNM Digital Repository Mathematics and Statistics Faculty and Staff Publications Academic Department Resources 2016 Various Arithmetic Functions and their Applications Florentin Smarandache University of New Mexico, [email protected] Octavian Cira Follow this and additional works at: https://digitalrepository.unm.edu/math_fsp Part of the Algebra Commons, Applied Mathematics Commons, Logic and Foundations Commons, Number Theory Commons, and the Set Theory Commons Recommended Citation Smarandache, Florentin and Octavian Cira. "Various Arithmetic Functions and their Applications." (2016). https://digitalrepository.unm.edu/math_fsp/256 This Book is brought to you for free and open access by the Academic Department Resources at UNM Digital Repository. It has been accepted for inclusion in Mathematics and Statistics Faculty and Staff Publications by an authorized administrator of UNM Digital Repository. For more information, please contact [email protected], [email protected], [email protected]. Octavian Cira Florentin Smarandache Octavian Cira and Florentin Smarandache Various Arithmetic Functions and their Applications Peer reviewers: Nassim Abbas, Youcef Chibani, Bilal Hadjadji and Zayen Azzouz Omar Communicating and Intelligent System Engineering Laboratory, Faculty of Electronics and Computer Science University of Science and Technology Houari Boumediene 32, El Alia, Bab Ezzouar, 16111, Algiers, Algeria Octavian Cira Florentin Smarandache Various Arithmetic Functions and their Applications PONS asbl Bruxelles, 2016 © 2016 Octavian Cira, Florentin Smarandache & Pons. All rights reserved. This book is protected by copyright. No part of this book may be reproduced in any form or by any means, including photocopying or using any information storage and retrieval system without written permission from the copyright owners Pons asbl Quai du Batelage no.
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Techsparx Java Tuitions
TechSparxJavaTuitionsTechSparxJavaJava Question Bank TuitionsTechSparxJavaTuitionsTechSp arxJavaTuitionsTechSparxJavaTuitions TechSparxJavaTuitionsTechSparxJavaTechSparx Java Tuitions “Better than a thousand days of diligent study is one day with a Great Teacher” TuitionsTechSparxJavaTuitionsTechSp Java Question Bank (version 5.3) arxJavaTuitionsTechSparxJavaTuitionshttp://techsparx.webs.com/ Saravanan.G TechSparxJavaTuitionsTechSparxJava TuitionsTech SparxJavaTuitionsTechSp arxJavaTuitionsTechSparxJavaTuitions TechSparxJavaTuitionsTechSparxJava TuitionsTechSparxJavaTuitionsTechSp arxJavaTuitionsTechSparxJavaTuitions TechSparxJavaTuitionsTechSparxJava TuitionsTechSparxJavaTuitionsTechSp arxJavaTuitionsTechSparxJavaTuitions TechSparxJavaTuitionsTechSparxJava TuitionsTechSparxJavaTuitionsTechSp Contents Modularization ........................................................................................................................................ 3 Most Simplest ......................................................................................................................................... 4 Decision Making Statements ................................................................................................................... 5 Switch Statement .................................................................................................................................... 6 Looping Constructs .................................................................................................................................
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Professor Stewart's Casebook of Mathematical Mysteries
Professor Stewart’s Casebook of Mathematical Mysteries Professor Ian Stewart is known throughout the world for making mathematics popular. He received the Royal Society’s Faraday Medal for furthering the public understanding of science in1995, the IMA Gold Medal in 2000, the AAAS Public Understanding of Science and Technology Award in 2001 and the LMS/IMA Zeeman Medal in 2008. He was elected a Fellow of the Royal Society in 2001. He is Emeritus Professor of Mathematics at the University of Warwick, where he divides his time between research into nonlinear dynamics and furthering public awareness of mathematics. His many popular science books include (with Terry Pratchett and Jack Cohen) The Science of Discworld I to IV, The Mathematics of Life, 17 Equations that Changed the World and The Great Mathematical Problems. His app, Professor Stewart’s Incredible Numbers, was published jointly by Profile and Touch Press in March 2014. By the Same Author Concepts Of Modern Mathematics Game, Set, And Math Does God Play Dice? Another Fine Math You’ve Got Me Into Fearful Symmetry Nature’s Numbers From Here To Infinity The Magical Maze Life’s Other Secret Flatterland What Shape Is A Snowflake? The Annotated Flatland Math Hysteria The Mayor Of Uglyville’s Dilemma How To Cut A Cake Letters To A Young Mathematician Taming The Infinite (Alternative Title: The Story Of Mathematics) Why Beauty Is Truth Cows In The Maze Mathematics Of Life Professor Stewart’s Cabinet Of Mathematical Curiosities Professor Stewart’s Hoard Of Mathematical Treasures Seventeen
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Different Types of Pretty Wild Narcissistic Numbers
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Intendd for Both
A DOCUMENT RESUME ED 040 874 SE 008 968 AUTHOR Schaaf, WilliamL. TITLE A Bibli6graphy of RecreationalMathematics, Volume INSTITUTION National Council 2. of Teachers ofMathematics, Inc., Washington, D.C. PUB DATE 70 NOTE 20ap. AVAILABLE FROM National Council of Teachers ofMathematics:, 1201 16th St., N.W., Washington, D.C.20036 ($4.00) EDRS PRICE EDRS Price ME-$1.00 HC Not DESCRIPTORS Available fromEDRS. *Annotated Bibliographies,*Literature Guides, Literature Reviews,*Mathematical Enrichment, *Mathematics Education,Reference Books ABSTRACT This book isa partially annotated books, articles bibliography of and periodicalsconcerned with puzzles, tricks, mathematicalgames, amusements, andparadoxes. Volume2 follows original monographwhich has an gone through threeeditions. Thepresent volume not onlybrings theliterature up to material which date but alsoincludes was omitted in Volume1. The book is the professionaland amateur intendd forboth mathematician. Thisguide canserve as a place to lookfor sourcematerials and will engaged in research. be helpful tostudents Many non-technicalreferences the laymaninterested in are included for mathematicsas a hobby. Oneuseful improvementover Volume 1 is that the number ofsubheadings has more than doubled. (FL) been 113, DEPARTMENT 01 KWH.EDUCATION & WELFARE OffICE 01 EDUCATION N- IN'S DOCUMENT HAS BEEN REPRODUCED EXACILY AS RECEIVEDFROM THE CO PERSON OR ORGANIZATION ORIGINATING IT POINTS Of VIEW OR OPINIONS STATED DO NOT NECESSARILY CD REPRESENT OFFICIAL OFFICE OfEDUCATION INt POSITION OR POLICY. C, C) W A BIBLIOGRAPHY OF recreational mathematics volume 2 Vicature- ligifitt.t. confiling of RECREATIONS F DIVERS KIND S7 VIZ. Numerical, 1Afironomical,I f Antomatical, GeometricallHorometrical, Mechanical,i1Cryptographical, i and Statical, Magnetical, [Htlorical. Publifhed to RecreateIngenious Spirits;andto induce them to make fartherlcruciny into tilde( and the like) Suut.tm2.
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Fixed and Flexible Powers Narcissistic Numbers with Division
Inder J. Taneja RGMIA Research Report Collection, 20(2017), pp.1-113, http://rgmia.org/v20.php Fixed and Flexible Powers Narcissistic Numbers with Division Inder J. Taneja1 Abstract This paper brings extension of narcissistic numbers with division. The extension is done in different sit- uations, such as, with positive and negative coefficients, fixed and flexible powers. Comparison with previous known numbers are also given. This is revised and enlarged version of author’s previous work [13]. Contents 1 Introduction 1 2 Fixed Power Narcissistic Numbers with Division 3 2.1 Fixed Power: Positive Coefficients . .3 2.2 Fixed Power: Positive and Negative Coefficients . .3 3 Flexible Power Narcissistic Numbers with Division 11 3.1 Flexible Power: Positive Coefficients . 11 3.2 Flexible Power: Positive and Negative Coefficients . 51 1 Introduction An n digit number that is the sum of the nth powers of its digits is called an n narcissistic number. It is ¡ ¡ also sometimes known as an Armstrong number, perfect digital invariant (Madachy 1966 [6]), or plus perfect number. Hardy in 1940 [2] (pg. 25) wrote, there are just four numbers of three digits, which are the sums of the cubes of their digits: 153 13 53 33 Æ Å Å 370 33 73 03 Æ Å Å 371 33 73 13 Æ Å Å 407 43 03 73 Æ Å Å The above four numbers have the same digits on both sides except the power 3 and are with 3 digits. There are four more numbers with 4 digits: 1634 : 14 64 34 44 Æ Å Å Å 4151 : 45 15 55 15 Æ Å Å Å 8208 : 84 24 04 84 Æ Å Å Å 9472 : 94 44 74 24 Æ Å Å Å 1Formerly, Professor of Mathematics, Universidade Federal de Santa Catarina, 88.040-900 Florianópolis, SC, Brazil.
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