On the diophantine equation x2-2m=±yn

One of the purposes of this note is to correct the proof of a recent result of Y. Guo & M. Le on the equation x(2) - 2(m) = y(n). Moreover, we prove that the diophantine equation x(2) - 2(m) = +/- y(n), x, y, m, n is an element of N, gcd(x, y) = 1, y > 1, n > 2 has only finitely many solutions, all of which satisfying n less than or equal to 7.310(5).