Journal of Integer Sequences, Vol. 14 (2011), Article 11.9.3

On Fibonacci and Lucas Numbers of the Form cx2

Refin Keskin and Zafer Yosma
Department of Mathematics
Facultyof Science and Arts
Sakarya University


In this paper, by using some congruences concerning with Fibonacci and Lucas numbers, we completely solve the Diophantine equations Ln = 2Lmx2, Fn = 2Fmx2, Ln = 6Lmx2, Fn = 3Fmx2, and Fn = 6Fmx2.

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(Concerned with sequence A000045.)

Received April 29 2011; revised version received August 18 2011; September 25 2011. Published in Journal of Integer Sequences, October 16 2011.

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