Statement: suppose a,b belongs to Z (integers). If 4/(a^2+b^2) then a and b are not both odd.
By proof of contradiction I assume that a and b are both odd.
If a^2 and b^2 is odd then by definition a and b must be odd too.
It follows that a^2 (or b^2) =(4k+1)^2 <- is this the correct way to show this?
Then a (or b) = 4k+1 <- is this the correct way to show this?
So if a and b are both odd then this is a contradiction hence the supposition is false and the statement is true.
I am wanting to show that a and b are both odd to fit the negation of the statement but I'm unsure about how to show that a and b are both odd in this case?