Weekly dose of number theory 1 (found this on mathpages.com)

Given three distinctive integers $a, b, c > 1$ such that $ab + 1 = 2x^2$ , $bc + 1 = 2y^2$ , $ca + 1 = 2z^2$ where $x, y, z$ are three integers to be found. Find the minimum of $a+b+c$ .