Three triads of integers with equal sums of squares and cubes

Abstract

While infinitely many examples of two triads of integers with equal sums of squares and cubes are known, until now there is no published example of three triads of integers with this property. In this paper we obtain, in parametric terms, three triads of integers with equal sums of squares and cubes and show that infinitely many similar parametric solutions for such triads can be obtained.