(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let a[itex]\in[/itex]Z. Prove that 3a+1 is even if and only if (a+1)/2 [itex]\in[/itex]Z

2. Relevant equations

We know that C is an odd number if there exists:

C=2k+1

Even:

C=2k

3. The attempt at a solution

I think I figured it out, but I'm terrible at Discrete Math, so I was hoping for some input. We know that:

3a+1=2k

If we want 3a+1 to be even. Given the extra constraint we have, I said:

3[(a+1)/2]+1=2k

After some simplification:

(3a+5)/2

I then factored out a positive 2 and:

2[(3a+5)/4]

From here:

(3a+5)/4=k

Therefor

2k=2k

Am I way off base here or is this actually correct?

Thanks! I have a bunch of homework problems due at the end of the week, so please be patient with me! This class is ruining my life...

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# Homework Help: Prove a Number is Even

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