On a sum of squares of integers in arithmetic progression

Abdullah Al Kafi Majumdar

doi:10.3329/jbas.v45i2.57321

On a sum of squares of integers in arithmetic progression

Authors

Abdullah Al Kafi Majumdar Beppu-shi Oaza Tsurumi, Renace Beppu, Beppu-shi, Japan

DOI:

https://doi.org/10.3329/jbas.v45i2.57321

Keywords:

Sum of squares, gcd, Arithmetic progression, Diophantine equation

Abstract

This paper derives the conditions under which the sum of squares of (2N+1) natural numbers in the arithmetic progression is a perfect square. It is shown that the problem leads to a Diophantine equation, which in turn indicates that there is, in fact, an infinite number of such numbers. Some particular cases are investigated.

J. Bangladesh Acad. Sci. 45(2); 241-250: December 2021

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Published

2022-01-26

How to Cite

Kafi Majumdar, A. A. (2022). On a sum of squares of integers in arithmetic progression. Journal of Bangladesh Academy of Sciences, 45(2), 241–250. https://doi.org/10.3329/jbas.v45i2.57321