The Proof of a Conjecture Related to Divisibility Properties
of z(n)
Keyword(s):
The order of appearance of n (in the Fibonacci sequence) z(n) is defined as the smallest positive integer k for which n divides the k—the Fibonacci number Fk. Very recently, Trojovský proved that z(n) is an even number for almost all positive integers n (in the natural density sense). Moreover, he conjectured that the same is valid for the set of integers n ≥ 1 for which the integer 4 divides z(n). In this paper, among other things, we prove that for any k ≥ 1, the number z(n) is divisible by 2k for almost all positive integers n (in particular, we confirm Trojovský’s conjecture).
Keyword(s):
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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2014 ◽
Vol 10
(04)
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pp. 915-933
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2011 ◽
Vol 07
(07)
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pp. 1959-1976
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Keyword(s):
2015 ◽
Vol 07
(01)
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pp. 1550001
2008 ◽
Vol 50
(1)
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pp. 27-32
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