Triads of integers with equal sums of squares and equal products and a related multigrade chain
Volume 178 / 2017
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.
