Number Theory

    

On the Finiteness of Sequences of Even Squarefree Fibonacci Numbers

Authors: Waldemar Puszkarz

Let 2p1p2 . . . pk−1 be an even squarefree Fibonacci number with k distinct prime factors. For each positive k, such numbers form an integersequence. We conjecture that each such sequence has only a finite number of terms. In particular, the factorization data for the first 1000 Fibonacci numbers suggests that there is only one such term for k = 2, 5 for k = 3, and 8 for k = 4. We also renew attention to the fact that a proof that there are infinitely many squarefree Fibonacci numbers remains lacking. Some approachto proving this, emerging from our study, is suggested.

Comments: 4 Pages. Originally posted on ResearchGate in December 2021.

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[v1] 2022-12-18 03:01:52

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