DETERMINATION OF TRIPLETS OF POSITIVE INTEGERS WITH SUM OF ANY TWO COORDINATES IS FIXED POWER OF INTEGER

In this article we discussed determination of distinct positive integers a, b, c such that a+b, a+c, b+c are cubes of positive integers, fourth powers of positive integers and such triplets are infinitely many. We can obtain infinitely many such triplets from a single triplet.

Using similar technique one can obtain infinitely many triplets of positive integers such that sum of any two terms of a triplet is nth power of a positive integer, where integer n ≥ 5.