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Triads of integers with equal sums of squares and equal products and a related multigrade chain

Volume 178 / 2017

Ajai Choudhry, Jarosław Wróblewski Acta Arithmetica 178 (2017), 87-100 MSC: Primary 11D09, 11D25; Secondary 11D41. DOI: 10.4064/aa8574-9-2016 Published online: 8 February 2017

Abstract

While the complete solution of the problem of finding two triads of integers with equal sums of squares and equal products is known, till now no examples of three such triads has been published. In this paper we find several triads of positive integers with equal sums of squares and equal products. We present several parametric solutions for three such triads and give numerical examples for five triads of integers with equal sums of squares and equal products. We use these triads to produce multigrade chains of quadruples of integers with equal sums of $k$th powers for $k=1,2,3,5$. We conclude the paper with some open problems concerning such triads.

Authors

  • Ajai Choudhry13/4 A Clay Square
    Lucknow 226001, India
    e-mail
  • Jarosław WróblewskiInstitute of Mathematics
    Wrocław University
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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