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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On regular polytope numbers
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by Hyun Kwang Kim PDF
Proc. Amer. Math. Soc. 131 (2003), 65-75 Request permission

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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 65-75
  • MSC (2000): Primary 11B13, 11B75, 11P05
  • DOI: https://doi.org/10.1090/S0002-9939-02-06710-2
  • MathSciNet review: 1929024