Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.7

Some Remarks On the Equation FnkFm In Fibonacci Numbers

M. Farrokhi D. G.
Faculty of Mathematical Sciences
Ferdowski University of Mashhad


Let {Fn}n= 1 = {1,1,2,3,...} be the sequence of Fibonacci numbers. In this paper we give some sufficient conditions on a natural number k such that the equation FnkFm is solvable with respect to the unknowns n and m. We also show that for k > 1 the equation FnkFm has at most one solution (n,m).

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(Concerned with sequence A000045.)

Received March 28 2007; revised version received May 22 2007. Published in Journal of Integer Sequences, June 4 2007.

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