THE FIBONACCI-NORM OF A POSITIVE INTEGER: OBSERVATIONS AND CONJECTURES
2010 ◽
Vol 06
(02)
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pp. 371-385
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In this paper, we define the Fibonacci-norm [Formula: see text] of a natural number n to be the smallest integer k such that n|Fk, the kth Fibonacci number. We show that [Formula: see text] for m ≥ 5. Thus by analogy we say that a natural number n ≥ 5 is a local-Fibonacci-number whenever [Formula: see text]. We offer several conjectures concerning the distribution of local-Fibonacci-numbers. We show that [Formula: see text], where [Formula: see text] provided Fm+k ≡ Fm (mod n) for all natural numbers m, with k ≥ 1 the smallest natural number for which this is true.
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2019 ◽
Vol 12
(03)
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pp. 1950046
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2018 ◽
Keyword(s):
2012 ◽
Vol 22
(4-5)
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pp. 614-704
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