On the Parity of the Order of Appearance in the Fibonacci Sequence
Let (Fn)n≥0 be the Fibonacci sequence. The order of appearance function (in the Fibonacci sequence) z:Z≥1→Z≥1 is defined as z(n):=min{k≥1:Fk≡0(modn)}. In this paper, among other things, we prove that z(n) is an even number for almost all positive integers n (i.e., the set of such n has natural density equal to 1).
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1938 ◽
Vol s2-44
(1)
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pp. 307-314
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1949 ◽
Vol s1-24
(1)
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pp. 4-13
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2006 ◽
Vol E89-A
(4)
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pp. 1132-1139
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