All integers except 23 and 239 are sums of eight cubes
نویسندگان
چکیده
منابع مشابه
q-Analogues of the Sums of Consecutive Integers, Squares, Cubes, Quarts and Quints
We first show how a special case of Jackson’s 8φ7 summation immediately gives Warnaar’s q-analogue of the sum of the first n cubes, as well as q-analogues of the sums of the first n integers and first n squares. Similarly, by appropriately specializing Bailey’s terminating very-well-poised balanced 10φ9 transformation and applying the terminating very-well-poised 6φ5 summation, we find q-analog...
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Euler noted the relation 63= 33+43+53 and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gennochi, Lucas, Pagliani, Cassels, Uchiyama, Stroeker and Zhongfeng Zhang. In particular, Stroeker determined all squares that can be written as a sum of at most 50 consecutive cubes. We generalize Stroeker’s work by determi...
متن کاملSums of Consecutive Integers
Wai Yan Pong ([email protected]) received his B.Sc. from the Chinese University of Hong Kong and his M.Sc. and Ph.D. from the University of Illinois at Chicago. He was a Doob Research Assistant Professor at the University of Illinois at Urbana-Champaign for three years. He then moved to California and is now teaching at California State University, Dominguez Hills. His research interests are in m...
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It is proved that, if F (x) be a cubic polynomial with integral coefficients having the property that F (n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F (x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F (n) is merely a...
متن کاملSums of squares, sums of cubes, and modern number theory
These are notes which grew out of a talk for general math graduate students with the aim of starting from the questions “Which numbers are sums of two squares?” and “Which numbers are sums of two cubes?” and going on a tour of many central topics in modern number theory. In the notes, I discuss composition laws, class groups, L-functions, modular forms, and elliptic curves, ending with the Birc...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1939
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1939-07041-9