Fibonacci Variations of a Conjecture of Polignac

Abstract

In 1849, Alphonse de Polignac conjectured that every odd positive integer can be written in the form 2n + p, for some integer n ≥ 0 and some prime p. In 1950, Erdős constructed infinitely many counterexamples to Polignac’s conjecture. In this article, we show that there exist infinitely many positive integers that cannot be written in either of the forms Fn + p or Fn− p, where Fn is a Fibonacci number, and p is a prime.

Cite this paper

@inproceedings{Jones2012FibonacciVO, title={Fibonacci Variations of a Conjecture of Polignac}, author={Lenny Jones}, year={2012} }