On a sum of squares of integers in arithmetic progression

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