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

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## Abstract

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).

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# Tatra Mountains Mathematical Publications

## The Journal of Slovak Academy of Sciences

### Journal Information

CiteScore 2017: 0.37

SCImago Journal Rank (SJR) 2017: 0.363
Source Normalized Impact per Paper (SNIP) 2017: 0.482

Mathematical Citation Quotient (MCQ) 2017: 0.14

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researchers in the all fields of mathematical research

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