Greetings

Prove that any integer $\displaystyle x>1$ has either a divisor $\displaystyle >1$ and $\displaystyle \leq\sqrt{x}$ or no divisor $\displaystyle >1$ and$\displaystyle \leq\sqrt{x}$ (In the latter case it is called a prime).

Prove this statement from the axioms governing the behavior of integers.