Jñānābha‎, Vol. 50 (2) (2020), (200-211)

A NEW APPROACH TO GENERATE FORMULAE FOR PYTHAGOREANS TRIPLES, QUADRUPLES AND THEIR GENERALISATION TO N-TUPLES

 

By

Narinder Kumar Wadhawan1* and Priyanka Wadhawan2

1*Civil Servant, Indian Administrative Service

Retired House No. 563, Panchkula-134112, Haryana, India.

Email: narinderkw@gmail.com

2Department Of Computer Sciences

Thapar Institute of Engineering and Technology, Patiala-134112, India.

Present Address : 2053 Courtyard Loop, Apt 207, Sanford, Florida, USA

Program Manager - Space Management (TCS)

Walgreen Co., 34, Wilmer Road, Deer Field II 60015, USA Email: priyanka.wadhawan@gmail.com

(Received : August 14, 2020 ; Revised: October 02, 2020)

 

 

In this paper, innovative methods have been devised to generate formulae for Pythagorean’s Triples, Quadruples and these are finally generalised to generate Pythagorean’s n-tuples. First method utilises formula for solution of a quadratic equation and generate two sets of Pythagorean’s Triples. Second method determines universal identities that satisfy Pythagorean’s Triples, Quadruples so on up to n-tuples. These methods are unprecedented, easy to derive at and hence are comprehensible to students and scholars alike.

 

2010 Mathematics Subject Classifications: Number Theory 11D09.

Keywords and phrases: Pythagorean Triples, Quadruples, Quintuples, Sextuples, Integers, n-tuples, Rational Numbers, Universal Identity.