Perfect powers that are sums of squares in a three term arithmetic progression

Angelos Koutsianas; Vandita Patel

doi:10.1142/S1793042118501646

Perfect powers that are sums of squares in a three term arithmetic progression

Angelos Koutsianas^*, Vandita Patel

^*Corresponding author for this work

Pure Mathematics

University of Piraeus

Research output: Contribution to journal › Article › peer-review

Abstract

We determine primitive solutions to the equation (x-r)² + x² + (x + r) ² = yn for 1 ≤ r ≤ 10⁴, making use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.

Original language	English
Pages (from-to)	2699-2728
Number of pages	30
Journal	International Journal of Number Theory
Volume	14
Issue number	10
DOIs	https://doi.org/10.1142/S1793042118501646
Publication status	Published - 1 Nov 2018

Keywords

Exponential equation
Lehmer sequences
primitive divisors

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10.1142/S1793042118501646

https://arxiv.org/pdf/1802.07485.pdf

Cite this

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title = "Perfect powers that are sums of squares in a three term arithmetic progression",

abstract = "We determine primitive solutions to the equation (x-r)2 + x2 + (x + r) 2 = yn for 1 ≤ r ≤ 104, making use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.",

keywords = "Exponential equation, Lehmer sequences, primitive divisors",

author = "Angelos Koutsianas and Vandita Patel",

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AU - Patel, Vandita

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AB - We determine primitive solutions to the equation (x-r)2 + x2 + (x + r) 2 = yn for 1 ≤ r ≤ 104, making use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.

KW - Exponential equation

KW - Lehmer sequences

KW - primitive divisors

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DO - 10.1142/S1793042118501646

M3 - Article

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JO - International Journal of Number Theory

JF - International Journal of Number Theory

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Perfect powers that are sums of squares in a three term arithmetic progression

Abstract

Keywords

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