Given an equation x^2+y^2+z^2=2010.
1. Prove that in every triplet of integers satisfying the above equation one number has to be even and two others odd.
2. How many integer solutions are there ?


Warning: 1 is very easy, 2 is quite tricky.

(In reply to re: solutions by broll)

I guess another way of looking at your point is that several values, such as 5 or 7, appear twice on the grid of non-trivially-varied solutions, and others only once, without regard to whether you consider them x values or y values or z values, as what you say about treating them as x values could be applied equally treating them as y or z values.

Posted by Charlie on 2010-11-05 10:51:40