Fibonacci Number Triples

where I=2(p-qb), m=2(p-gqa), a= l (1 + \15), b-(1-\/5). The purpose of this article is to find a connection between generalized Fibonacci numbers and Pythagorean number triples. By a Pythagorean (number) triple is meant a set of three mutually prime integers u, v, w for which u2+v2 = w2. The problem to be solved is this: Given such a triple u, v, w, can we find n, p, q such that the integers whose squares appear in (3) below are these u, v, w? The answer is yes. Viewed in this light, Pythagorean triples may be called Fibonacci (number) triples.