How to express that $y$ is a natural number and $x$ is an odd natural number in a compact language? I have this expression
$ \frac {x^2}{y}$ for all $y\in\mathbb{N}$ and only odd values of $x\in\mathbb{N}$. Is it possible to express these assumptions (especially that $x$ is odd) in a compact mathematical language?

I mean if I want to use this sentence
" $ \frac {x^2}{y}$ with $x,y\in\mathbb{N}$ ",
what should I add to this sentence to express that $x$ is odd?


$x$ is odd implies that $x = 2n+1$ for $n \in \Bbb N$
$x=2n-1$ also works
Why that? because odd numbers are one less or one more than the even numbers and even numbers are of the form $x = 2n$
You should add "$(x,y)\in \Bbb N\space \text{and}\space x = 2n+1\space \text{for some}\space n\in \Bbb N$" to your solution/statement
