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show that $4k+2$ is not a square of a natural number

I don't know how to start with this problem.

I thought that maybe $(4k+2)^2=4(4k^2+4k+1)$ help me but I don't know what to do next.

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2 Answers 2

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$4k+2 = 2(2k+1)$. It can't be a square because it is divisible by $2$ but not by $4$ ($2k+1$ is odd).

Hope that helps,

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Hint: $2 \mid 2(2k+1)$, but $2^2 \not\mid 2(2k+1)$.

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