Hello all I've been practicing proofs and would like to know if I'm on the right track. Here it is:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Proof of different parities

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