Perfect Powers that are Sums of Squares of an Arithmetic Progression

Debanjana Kundu; Vandita Patel

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arXiv · 1809.09167

Perfect Powers that are Sums of Squares of an Arithmetic Progression

Debanjana Kundu·Vandita Patel

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Abstract

In this paper, we determine all primitive solutions to the equation $(x+r)^2 +(x+2r)^2 +\cdots +(x+dr)^2 = y^n$ for $2\leq d\leq 10$ and for $1\leq r\leq 10^4$. We make use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.

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Debanjana Kundu, Vandita Patel. 2018-09-24. Perfect Powers that are Sums of Squares of an Arithmetic Progression. https://arxiv.org/abs/1809.09167

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