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

J. N. SALUNKE *

SRTM University, Nanded, India.

P. M. AMBULGE

SRTM University, Nanded, India.

*Author to whom correspondence should be addressed.

### Abstract

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.

Keywords: Perfect square, Four tuple, Congruence relation, divisibility

#### How to Cite

*Asian Journal of Mathematics and Computer Research*,

*15*(1), 56–70. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/719