Almost universal ternary sums of triangular numbers

Chan, Wai Kiu; Oh, Byeong-Kweon

doi:10.1090/S0002-9939-09-09990-0

Almost universal ternary sums of triangular numbers
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by Wai Kiu Chan and Byeong-Kweon Oh PDF

Proc. Amer. Math. Soc. 137 (2009), 3553-3562 Request permission

Abstract:

For any integer $x$, let $T_x$ denote the triangular number $\frac {x(x+1)}{2}$. In this paper we give a complete characterization of all the triples of positive integers $(\alpha , \beta , \gamma )$ for which the ternary sums $\alpha T_x + \beta T_y + \gamma T_z$ represent all but finitely many positive integers, which resolves a conjecture of Kane and Sun.

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