Fermat's polygonal number theorem for repeated generalized polygonal numbers

Soumyarup Banerjee,Manav Batavia,Ben Kane,Muratzhan Kyranbay,Dayoon Park,Sagnik Saha,Hiu Chun So,Piyush Varyani

doi:10.1016/j.jnt.2020.05.024

Fermat's polygonal number theorem for repeated generalized polygonal numbers

Soumyarup Banerjee, Manav Batavia + Show 6 more

Open Access

https://doi.org/10.1016/j.jnt.2020.05.024

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Journal: Journal of number theory

Publication Date: Jul 20, 2020

Affiliation: University of Hong Kong, Indian Institute of Technology Bombay, Hong Kong Baptist University, Seoul National University, Indian Institute of Science Education and Research, Thiruvananthapuram, Indian Institute of Technology Roorkee

#Polygonal Number #Fermat's Theorem + Show 3 more

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Abstract

TextIn 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. VideoFor a video summary of this paper, please visit https://youtu.be/WRb91yye-IQ.

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