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Fibonacci Variations of a Conjecture of Polignac

Lenny Jones
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2011-0126


In 1849, Alphonse de Polignac conjectured that every odd positive integer can be written in the form , for some integer 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 or , where is a Fibonacci number, and p is a prime.

Keywords: Fibonacci Number; Prime Number; Polignac

About the article

Received: 2010-09-17

Revised: 2011-06-16

Accepted: 2012-01-10

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 659–667, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2011-0126.

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