Mathematical Reviews on the Web C Copyright American Mathematical Society 2004
Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 2004 1 997 583 11J68 11R06 Borwein, Peter (3-SFR-MS); Hare, Kevin G. (3-SFR-MS) Non-trivial quadratic approximations to zero of a family of cubic Pisot numbers. (English. English summary) Trans. Amer. Math. Soc. 355 (2003), no. 12, 4767–4779 (electronic). 1 986 822 11D72 11P05 11Y50 Borwein, Peter (3-SFR); Lisonˇek,Petr (3-SFR); Percival, Colin (3-SFR) Computational investigations of the Prouhet-Tarry-Escott problem. (English. English summary) Math. Comp. 72 (2003), no. 244, 2063–2070 (electronic). The Prouhet-Tarry-Escott problem asks for two distinct multisets of integers X = {x1, . , xn} and Y = {y1, . , yn} such that n n X e X e xi = yi i=1 i=1 for e = 1, 2, . , k for some integer k < n. If k = n − 1, such a solution is called ideal. The authors describe a method for searching for ideal symmetric solutions. They make an extensive search for solutions up to n = 12. They find two new solutions for n = 10, which are much smaller than the solutions found by A. Letac in the 1940s. Maurice Mignotte (F-STRAS) 1 986 811 11C08 30C10 Borwein, P. B. (3-SFR-MS); Pinner, C. G. (1-KSS); Pritsker, I. E. (1-OKS) Monic integer Chebyshev problem. (English. English summary) Math. Comp. 72 (2003), no. 244, 1901–1916 (electronic). Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 2004 2004a:11069 11J72 11J82 33D15 41A21 Borwein, Peter B. (3-SFR-MS); Zhou, Ping [Zhou, Ping2] (3-SFX-MSC) On the irrationality of a certain multivariate q series.
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