Parameterize the solutions in integers to x^2 + 5y^2 = z^2 in Pythagorean triples.
To make it easier, consider only the solutions such that (x,y,z)=1. Also assume that x, y, and z are positive, and that x is odd. Your analysis will probably give you two cases, but you can combine them into one by use of absolute values. Naturally, prove that your analysis is correct.
Can anyone solve the above question?