How to denote an even number in mathematics?

Question

I need a sign for an even number (not $a\cdot 2$) in my formula. I tried to google it, but I saw only $2a$. Please tell me if there is a special sign?

Answer 1

As denoted in the answer to this question: Is zero odd or even?, $N_e$ is used to denote even numbers and $N_o$ for odd numbers. However, you could use any notation as long as it's clear to the reader what you are trying to symbolize with it.

Answer 2

We often like to say that an even number is any $2k$ for $k\in \mathbb Z$.

But another way is to use $\mathbb Z$ with scalar multiplication.

I.e. $\mathbb Z = \{..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...\}$. You know. The integers.

So $2\mathbb Z = \{..., -8, -6, -4, -2, 0, 2, 4, 6, 8, ...\}$ because every element in $\mathbb Z$ gets multiplied by $2$. This is now the set of all even numbers.

Now, you can refer to a number $n$ as even if $n \in 2\mathbb Z$.