在等差数列的整数平方和上

Journal of Bangladesh Academy of Sciences Pub Date : 2022-01-26 DOI:10.3329/jbas.v45i2.57321

Abdullah Al Kafi Majumdar

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摘要

本文导出了等差数列中(2N+1)个自然数的平方和为完全平方的条件。结果表明，这个问题导致丢番图方程，而丢番图方程反过来又表明，事实上有无限个这样的数。对一些特殊案例进行了调查。科学通报，2011 (2);241-250: 2021年12月

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On a sum of squares of integers in arithmetic progression

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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Journal of Bangladesh Academy of Sciences

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