TERNAS PITAGÓRICAS E SEQUÊNCIAS NUMÉRICAS: NOVOS RESULTADOS

Abstract

Using an interdisciplinary approach, we present solutions within the class of Pythagorean triples problems for three cases. More precisely, we prove cases of existence and non-existence of Pythagorean triples involving Arithmetic Progressions, Geometric Progressions, and the Fibonacci Sequence. We show that, in the case of Arithmetic Progressions, the only Pythagorean triples are generated by a famous triple. In the case of GPs and the Fibonacci Sequence, we prove the non-existence of Pythagorean triples of positive integers, even when the terms are not consecutive. To the best of our knowledge, the answers to the problems established here for the GPs and the Fibonacci Sequence are original. This work is a consequence of the studies from a professional master's dissertation (PROFMAT-UFRPE), in which we present some classical results on numerical sequences and their applications.

Keywords: Pythagorean Triples; Arithmetic Progression; Geometric Progression; Fibonacci Sequence; PROFMAT.