COMPUTATIONAL ALGORITHM FOR SOLVING THE DIOPHANTINE EQUATIONS 2n ± α . 2m + α2 = x2

In this paper, we construct an algorithm for solving the diophantine equations 2(n) +/- alpha . 2(m) + alpha(2) = x(2), where a is a given odd prime such that 2 is a non-quadratic residue modulo a. Applying the implementation of the procedure in Maple, apart from the plus case with the condition n < m we solve completely the problem for alpha < 3 . 10(6). The theoretical background relies on the treatment worked out to solve the equation 2(n) + 2(m) + 1 = x(2).