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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On regular polytope numbers


Author: Hyun Kwang Kim
Journal: Proc. Amer. Math. Soc. 131 (2003), 65-75
MSC (2000): Primary 11B13, 11B75, 11P05
Published electronically: June 12, 2002
MathSciNet review: 1929024
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Abstract: Lagrange proved a theorem which states that every nonnegative integer can be written as a sum of four squares. This result can be generalized as the polygonal number theorem and the Hilbert-Waring problem. In this paper, we shall generalize Lagrange's sum of four squares theorem further. To each regular polytope $V$ in a Euclidean space, we will associate a sequence of nonnegative integers which we shall call regular polytope numbers, and consider the problem of finding the order $g(V)$ of the set of regular polytope numbers associated to $V$.


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Additional Information

Hyun Kwang Kim
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784 Korea
Email: hkkim@postech.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06710-2
PII: S 0002-9939(02)06710-2
Received by editor(s): August 20, 2001
Published electronically: June 12, 2002
Additional Notes: This work was supported by Com$^{2}$MaC-KOSEF
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2002 American Mathematical Society