ON FOUR TUPLE IN N4 WITH THE SUM OF SOME COORDINATES IS A PERFECT SQUARE

In this article we determine infinitely many families of four tuples of positive integers such that in each of these four tuples sum of any three coordinates is a perfect square. We have obtained families of such four tuples where all coordinates in each tuple are equal / exactly three coordinates are equal / exactly two coordinates are equal / all coordinates are distinct.

We also discussed a technique to determine a four tuple of positive integers such that sum of any two coordinate is a perfect square. We have obtained families of such four tuples such that in which all coordinates are equal / exactly three coordinates are equal / exactly two coordinates are equal / all coordinates are distinct.