INFINITELY MANY POSITIVE INTEGER SOLUTIONS OF THE QUADRATIC DIOPHANTINE EQUATIONS x 2 − 8 B
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چکیده
In this study, we consider the quadratic Diophantine equations given in the title and determine when these equations have positive integer solutions. Moreover, we find all positive integer solutions of them in terms of Balancing numbers Bn, Pell and Pell-Lucas numbers, and the terms of the sequence {vn} , where {vn} is defined by v0 = 2, v1 = 6, and vn+1 = 6vn − vn−1 for n ≥ 1.
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تاریخ انتشار 2014