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Some Remarks On the Equation
***F*_{n} = *kF*_{m}
In Fibonacci Numbers

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M. Farrokhi D. G.

Faculty of Mathematical Sciences

Ferdowski University of Mashhad

Iran

**Abstract:**

Let {*F*_{n}}_{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
*F*_{n} = *kF*_{m}
is solvable with respect to the unknowns *n* and *m*.
We also show that for *k* > 1 the equation
*F*_{n} = *kF*_{m}
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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