Fermat's polygonal number theorem for repeated generalized polygonal numbers

2019/08/06 by Banerjee, Soumyarup, Batavia, Manav, Kane, Ben +5
#11E08 #11E12 #11E25 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.02102

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 m-gonal numbers required to represent every positive integer and we furthermore generalize this result to obtain optimal bounds when many of the generalized m-gonal numbers are repeated r times, where r∈ℕ is fixed.

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