Prove that $a$ is always odd for when $a \% 2=1$

Question

'%' is a common way of writing 'modulo' (or more strictly 'remainder') in lots of programming languages.

I have a simple formula: $a \% 2=1$

I have to prove that $a$ will always be an odd integer, but not sure how to write it out. I can prove by example, for example, substituting an integer into $a$, but that is not proving it.

Answer 1

If $a$ is $1\pmod2$, then, by definition, $a=1+2k$, for some $k\in\Bbb Z$. But that makes $a$ odd.