A NEW APPROACH TO GENERATE FORMULAE FOR PYTHAGOREANS TRIPLES, QUADRUPLES AND THEIR GENERALISATION TO N-TUPLES
Narinder Kumar Wadhawan1* and Priyanka Wadhawan2
1*Civil Servant, Indian Administrative Service
Retired House No. 563, Panchkula-134112, Haryana, India.
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: firstname.lastname@example.org
(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.
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