Some Remarks On the Equation
Fn = kFm
In Fibonacci Numbers
M. Farrokhi D. G.
Faculty of Mathematical Sciences
Ferdowski University of Mashhad
Iran
Abstract:
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
Fn = kFm
is solvable with respect to the unknowns n and m.
We also show that for k > 1 the equation
Fn = kFm
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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