Logical representation of a divisor using only $(=, <, \cdot)$

Question

$x$ is a divisor of $y$ (symbols: $=, <, \cdot$) for $\mathbb{N}$.

Does it make sense?

$(\forall y \in \mathbb{N} \quad \exists x,p \in \mathbb{N})(( y = x \cdot p) \wedge (x < y))$

Answer 1

If I understand what you're asking, then $x$ is a divisor of $y$ is equivalent, $\exists n \in \mathbb{N}$ such that $y=xn$. Sometimes such that is just indicated with a ,. That's it.