The Order of Appearance of the Product of Five Consecutive Lucas Numbers
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11. März 2015
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Online veröffentlicht: 11. März 2015
Seitenbereich: 65 - 77
Eingereicht: 02. Sept. 2014
DOI: https://doi.org/10.2478/tmmp-2014-0019
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© 2015
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Let Fn be the nth Fibonacci number and let Ln be the nth Lucas number. The order of appearance z(n) of a natural number n is defined as the smallest natural number k such that n divides Fk. For instance, z(Fn) = n = z(Ln)/2 for all n > 2. In this paper, among other things, we prove that
for all positive integers n ≡ 0,8 (mod 12).