DETERMINATION OF TRIPLETS OF POSITIVE INTEGERS WITH SUM OF ANY TWO COORDINATES IS FIXED POWER OF INTEGER
JAGANNATH N. SALUNKE
School of Mathematical Sciences, SRTM University, Nanded, 431606 Maharashtra, India
SACHIN P. BASUDE *
School of Mathematical Sciences, SRTM University, Nanded, 431606 Maharashtra, India
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Perfect squares, triplet of positive integers