The number of representations by a ternary sum of triangular numbers

2018/01/15 by Kim, Mingyu, Oh, Byeong-Kweon
#11E12 #11E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.04836

Abstract

For positive integers a,b,c, and an integer n, the number of integer solutions (x,y,z) ∈ \mathbb Z³ of a (x(x-1))/(2) + b (y(y-1))/(2) + c (z(z-1))/(2) = n is denoted by t(a,b,c;n). In this article, we prove some relations between t(a,b,c;n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in \cites.

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