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On the sums of three generalized polygonal numbers
Published 6 Jun 2018 in math.NT | (1806.02105v3)
Abstract: For each natural number $m\ge 3$, let $P_m(x)$ denote the generalized $m$-gonal number $\frac{(m-2)x2-(m-4)x}{2}$ with $x\in\mathbb{Z}$. In this paper, with the help of the congruence theta function, we establish conditions on $a$, $b$, $c$ for which the sum $P_a(x)+P_b(y)+P_c(z)$ represents all but finitely many positive integers.
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