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Analogues of two classical theorems on the representations of a number. (English) Zbl 1202.11025
Summary: Jacobi’s classical four-square theorem gives the number of representations of a positive integer as the sum of four squares. A theorem of Legendre gives the number of representations of a positive integer as the sum of four triangular numbers. In this paper we give analogous results that involve triangular numbers, squares, pentagonal numbers, and octagonal numbers.

MSC:
11D85 Representation problems
11D09 Quadratic and bilinear Diophantine equations
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