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This question already has an answer here:

I have noticed that it is useful to treat $0$ as an even number, and do so. Especially for patterns, puzzles, etc, if I develop a formula that works for something, and uses the parity of the number, then for my formula to work for something, I usually need to treat $0$ as even.

Is $0$ treated as an even number?

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marked as duplicate by Henning Makholm, Dando18, Sahiba Arora, Hans Lundmark, Xam Aug 1 '17 at 19:19

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  • $\begingroup$ Yes, it is. An even number, by definition, is divisible by $2$. $\endgroup$ – Alvin Lepik Aug 1 '17 at 14:35
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    $\begingroup$ Googling it would take you literally 1 second. And you would immediately find answer on Wikipedia. $\endgroup$ – windircurse Aug 1 '17 at 14:41
  • $\begingroup$ Is there some integer $k$ such that $2k=0$? Yes, so zero is even. Of course there are always situations where a positive number is needed, in which case $0$ would not be a suitable value. $\endgroup$ – Joffan Aug 1 '17 at 14:42
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Yes, since $2 (0) = 0$. Any integer evenly divisible by 2 is even.

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Yes, it is. So if $2 \mid x$, we call $x$ even.

And obviously, $2 \mid 0$.

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The way we define a even number is as follows $$x\ is\ even \Leftrightarrow\exists k\in\mathbf{Z}(x=2k)$$ evidently $0=2(0)$ so yes $0$ is even.

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$0$ is an integer multiple of 2.

But the zero function $f$ such that $\forall x\in \mathbb{R}, f(x)=0$ is odd and even!

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