A Diophantine System

2019/08/26 by Ajai Choudhry, Choudhry, Ajai
Mathematics · Physics and Astronomy · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.1908.09742

Abstract

In this paper we find a parametric solution to the hitherto unsolved problem of finding three positive integers such that their sum, the sum of their squares and the sum of their cubes are simultaneously perfect squares.

Related

• Three integers whose sum, product and the sum of the products of the integers, taken two at a time, are perfect squares
• Simultaneous equal sums of three powers
• An Elementary Approach For Sums Of Consecutive Cubes Being Prime Power Squares
• The problem of finding three numbers such that the sum or difference of any two of them is a square number
• Perfect powers in alternating sum of consecutive cubes