1. The problem statement, all variables and given/known data i want to prove that x is even in this equation 2^x+3^y=z^2 (1) 2. Relevant equations 3. The attempt at a solution what i have so far is (1) is congruent to mod3 2^x=z^2(mod3) when z=1 and x=2 then 4=1(mod3) so therefore x is even? have i proved that x is even, or am i missing anything?