Fibonacci Number Triples

  title={Fibonacci Number Triples},
  author={A. F. Horadam},
  journal={American Mathematical Monthly},
  • A. F. Horadam
  • Published 1961
  • Mathematics
  • American Mathematical Monthly
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… Expand
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