How to Write a Direct Proof (the product of odd integers is odd)

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[cassandriel]

When I first started, I couldn't understand how (2mn+m+n) could just be written off as k. It turns out the reason you can do that is because earlier we designated m and n as any integer. So, it doesn't matter what (2mn+m+n) results in. This meant that it can take the form of k giving us 2k+1.

[clarencebrosoto]

What If x3 and y3 are odd, then (xy)3 is odd