Exact Divisibility by Powers of the Fibonacci and Lucas Numbers
Prapanpong Pongsriiam
Department of Mathematics, Faculty of Science
Silpakorn University
Ratchamankanai Rd, Nakhon Pathom
Thailand, 73000
Abstract:
We give new results on exact divisibility by powers of the Fibonacci
and Lucas numbers. For example, we prove that if Fnk exactly divides m
and n is not congruent to 3 modulo 6,
then Fnk+1 exactly divides
Fnm. We
also provide some examples and open questions.
Full version: pdf,
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(Concerned with sequences
A000032
A000045.)
Received July 24 2014;
revised version received November 5 2014; November 6 2014.
Published in Journal of Integer Sequences, November 7 2014.
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