Journal of Integer Sequences, Vol. 17 (2014), Article 14.11.2

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


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,    dvi,    ps,    latex    

(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.

Return to Journal of Integer Sequences home page