Melham, R. S. Analogues of two classical theorems on the representations of a number. (English) Zbl 1202.11025 Integers 8, No. 1, Article A51, 10 p. (2008). 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. Cited in 1 Document MSC: 11D85 Representation problems 11D09 Quadratic and bilinear Diophantine equations PDFBibTeX XMLCite \textit{R. S. Melham}, Integers 8, No. 1, Article A51, 10 p. (2008; Zbl 1202.11025) Full Text: EuDML EMIS