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arXiv · 2409.07895

Sums of generalized polygonal numbers of almost prime "length"

Soumyarup Banerjee·Ben Kane·Daejun Kim
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Abstract

In this paper, we consider sums of three generalized $m$-gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions on $m$ modulo $30$, we show that a density one set of integers is represented as such a sum, where the parameters are restricted to have at most 6361 prime factors. Moreover, if the squarefree part of $f_m(n)$ is sufficiently large, then $n$ is represented as such a sum, where $f_m(n)$ is a natural linear function in $n$.

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Soumyarup Banerjee, Ben Kane, Daejun Kim. 2024-09-12. Sums of generalized polygonal numbers of almost prime "length". https://arxiv.org/abs/2409.07895

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