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

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Published: 2017-01-26

Page: 56-70


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

SALUNKE, J. N., & AMBULGE, P. M. (2017). ON FOUR TUPLE IN N4 WITH THE SUM OF SOME COORDINATES IS A PERFECT SQUARE. Asian Journal of Mathematics and Computer Research, 15(1), 56–70. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/719

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