Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On regular polytope numbers

Author(s): Hyun Kwang Kim
Journal: Proc. Amer. Math. Soc. 131 (2003), 65-75.
MSC (2000): Primary 11B13, 11B75, 11P05
Posted: 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 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 of the set of regular polytope numbers associated to .

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