1. The problem statement, all variables and given/known data given the equality a2+b2+c2+d2+e2=f2 prove 2 out of the the 6 variables must be even. 2. Relevant equations can use quadratic residues and primitive roots if it helps but don't think i need them. 3. The attempt at a solution assume f is even. then f2 is even. and not all 5 numbers on the left can be odd or else we would have odd=even. so at least one even on the LHS completes this case. assume f is odd. then f2 is odd. so the LHS must have a odd number of odd numbers. 1,3,5 of these numbers must be odd. if it's 1,3 then we have at least 2 even and are done. so now i need to prove by contradiction that not all 5 can be odd. this is where i am stuck and am thinking maybe the whole method is wrong. a hint would be nice, thanks.