Hello all I've been practicing proofs and would like to know if I'm on the right track. Here it is: If the sum of 3x + 3y is an odd number then x and y are different parities. Proof: Let x and y be two integers with opposite parity. Without loss of generality, suppose x is even and y is odd: x = 2m y = 2n + 1 Then: 3x + 3y = 3(2m) + 3(2n + 1) = 6m + 6n + 1 = 2(3m + 3n) + 1 Since 2(3m + 3n) has a factor of 2 it is even. When 1 is added, 2(3m + 3n) + 1 is odd. Therefore, 3x + 3y is odd and x and y have opposite parities. Is this enough or do I need more?