On a conjecture of Sun

Abstract

A number of the form x(x+1)/2 where x is an integer is called a triangular number. Suppose,, respectively. Z.-H. Sun, in [16], conjectured some relations between T (a, b, c; n) and N (a, b, c; 8n + a + b + c). In this paper, we prove these conjectures using theta function identities. Moreover, we add some new triplets (a, b, c) satisfying these conjectures.