Fermat's polygonal number theorem for repeated generalized polygonal numbers
Number Theory
2020-05-11 v4 Combinatorics
Abstract
In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized -gonal numbers required to represent every positive integer and we furthermore generalize this result to obtain optimal bounds when many of the generalized -gonal numbers are repeated times, where is fixed.
Cite
@article{arxiv.1908.02102,
title = {Fermat's polygonal number theorem for repeated generalized polygonal numbers},
author = {Soumyarup Banerjee and Manav Batavia and Ben Kane and Muratzhan Kyranbay and Dayoon Park and Sagnik Saha and Hiu Chun So and Piyush Varyani},
journal= {arXiv preprint arXiv:1908.02102},
year = {2020}
}