[seqfan] Magic Multipliers

Hans Havermann gladhobo at teksavvy.com
Fri Apr 4 15:47:51 CEST 2014


I first empirically formulated this in a message here two months ago [February 12, Re: More (composite) terms for A233281]. I am still sufficiently entranced by these "multipliers" that I have proposed A240239 to enumerate them. I'll encapsulate my strictly non-mathematical understanding of these numbers:

The prime factors of a composite Fibonacci(p), p prime, are all one less, or one more, than an even multiple of p. For a given factor of F(p), let m be one half of that even multiple. If m is odd, the factor is 2mp-1. If m is even, the factor is 2mp+1. Why? What property of p (other than the one just stated) predicts this dichotomy? Prove (or disprove): m is never an odd multiple of 5.


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