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 $V$.References
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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