- #1

songoku

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- Homework Statement:
- Prove that if ##n^2## is multiple of 2 then n is multiple of 2 (n is integer)

- Relevant Equations:
- Multiple of 2 = 2k

This is what I did:

If n is multiple of 2, then n can be stated in the form of 2k, where k is integer. So:

$$n^2=(2k)^2=4k^2=2(2k^2)$$ means that ##n^2## is multiple of 2

But I am pretty sure my working is wrong because I think what I did is the other way around, proving ##n^2## is multiple of 2 if ##n## is multiple of 2

How to do direct proof for this question? Thanks

If n is multiple of 2, then n can be stated in the form of 2k, where k is integer. So:

$$n^2=(2k)^2=4k^2=2(2k^2)$$ means that ##n^2## is multiple of 2

But I am pretty sure my working is wrong because I think what I did is the other way around, proving ##n^2## is multiple of 2 if ##n## is multiple of 2

How to do direct proof for this question? Thanks