The Order of Appearance of the Product of Five Consecutive Lucas Numbers

Marques, Diego; Trojovský, Pavel

doi:10.2478/tmmp-2014-0019

Abstract

Let F_n be the nth Fibonacci number and let L_n 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(F_n) = n = z(L_n)/2 for all n > 2. In this paper, among other things, we prove that

for all positive integers n ≡ 0,8 (mod 12).

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The Order of Appearance of the Product of Five Consecutive Lucas Numbers

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