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Homework Statement
given the equality a2+b2+c2+d2+e2=f2
prove 2 out of the the 6 variables must be even.
Homework Equations
can use quadratic residues and primitive roots if it helps but don't think i need them.
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.
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