Fibonacci Variations of a Conjecture of Polignac

Fibonacci Variations of a Conjecture of Polignac

In 1849, Alphonse de Polignac conjectured that every odd positive integer can be written in the form , for some integer and some prime . In 1950, Erdős constructed infinitely many counterexamples to Polignac's conjecture. In this article, we show that there exist infinitely many positive intege...

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Veröffentlicht in:Integers (Berlin, Germany) Germany), 2012-08, Vol.12 (4), p.659-667
1. Verfasser: Jones, Lenny
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Fibonacci Number
Polignac
Prime Number
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description In 1849, Alphonse de Polignac conjectured that every odd positive integer can be written in the form , for some integer and some prime . 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 is a prime.
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subjects Fibonacci Number
Polignac
Prime Number
title Fibonacci Variations of a Conjecture of Polignac
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