N!be = n!a (Contradiction)

a and b are integers. $$n!be = n!a$$ for every $$n \geq 0 \Rightarrow$$ Contradiction

Explanation

$$n!a$$ is an integer, for every value of n.

$$n!be$$ is not an integer, for some value of n. (more)

$$n!be \neq n!a$$ for some value of n.