Abstract
This paper aims to construct a new formula that generates a Fibonacci numbers in a generalized Pythagorean triples. In addition, the paper formulates some Fibonacci identities and discuss some important findings.
Highlights
Through various years, Fibonacci's famous number sequence has been a source of a lot of intriguing mathematical investigations and researches [14]
Several mathematicians are inspired of dealing Fibonacci identities that can be proven by induction, generating functions, determinants and so on [2, 3, 14, 16]
Several mathematicians studied the deep connection of Fibonacci numbers and Pythagorean triples which resulted to numerous papers in literature [10, 12, 13, 14]
Summary
Fibonacci's famous number sequence has been a source of a lot of intriguing mathematical investigations and researches [14]. Another paper of Casinillo and Casinillo [7] generates a new formula for generalized version of congruent numbers based on a generalized version of Pythagorean triples. Several mathematicians studied the deep connection of Fibonacci numbers and Pythagorean triples which resulted to numerous papers in literature [10, 12, 13, 14]. The purpose of this paper is to construct a new formula that generates a Fibonacci numbers in a generalized version of Pythagorean triples.
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