Open AccessOn a sum of squares of integers in arithmetic progression
Author(s) -
A. A. K. Majumdar
Publication year - 2022
Publication title -
journal of bangladesh academy of sciences
Language(s) - English
Resource type - Journals
eISSN - 2224-7270
pISSN - 0378-8121
DOI - 10.3329/jbas.v45i2.57321
Subject(s) - diophantine equation , mathematics , arithmetic progression , natural number , arithmetic , square (algebra) , diophantine set , square number , combinatorics , discrete mathematics , geometry
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