Almost universal ternary sums of triangular numbers

2009/07/27 by Wai Kiu Chan, Byeong-Kweon Oh · 3 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Rings, Modules, and Algebras

paper · pdf · doi:10.1090/s0002-9939-09-09990-0

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 (α , β , γ ) for which the ternary sums α T_x + β T_y + γ T_z represent all but finitely many positive integers, which resolves a conjecture of Kane and Sun.

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• Ternary Sums of Squares and Triangular Numbers
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