Open AccessSOME NOTES ON A GENERALIZED VERSION OF PYTHAGOREAN TRIPLES
Author(s) -
Leomarich F. Casinillo,
Emily L. Casinillo
Publication year - 2020
Publication title -
jurnal riset dan aplikasi matematika (jram)
Language(s) - English
Resource type - Journals
ISSN - 2581-0154
DOI - 10.26740/jram.v4n2.p103-107
Subject(s) - pythagorean triple , diophantine equation , pythagorean theorem , combinatorics , mathematics , prime (order theory) , coprime integers , prime number , set (abstract data type) , discrete mathematics , computer science , geometry , programming language
A Pythagorean triple is a set of three positive integers a, b and c that satisfy the Diophantine equation a^2+b^2=c^2. The triple is said to be primitive if gcd(a, b, c)=1 and each pair of integers and are relatively prime, otherwise known as non-primitive. In this paper, the generalized version of the formula that generates primitive and non-primitive Pythagorean triples that depends on two positive integers k and n, that is, P_T=(a(k, n), b(k, n), c(k, n)) were constructed. Further, we determined the values of k and n that generates primitive Pythagorean triples and give some important results.