|Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.6|
University of Debrecen
4010 Debrecen, PO Box 12
We illustrate this approach with a particular application of finding near-multiples of squares in Lucas sequences. As an example, we establish that among Fibonacci numbers only 2 and 34 are of the form 2m2+2; only 1, 13, and 1597 are of the form m2-3; and so on.
As an auxiliary result, we also give an algorithm for solving a Diophantine equation k^2 = f(m,n)/g(m,n) in integers m, n, k, where f and g are homogeneous quadratic polynomials.
(Concerned with sequences
Received February 22 2014; revised version received May 17 2014. Published in Journal of Integer Sequences, May 18 2014.