Another Good Number?

True or False?

If $$a^n - b^n$$ is an integer for all natural $$n$$ and distinct real numbers $$a,b$$, then $$a$$ and $$b$$ must be integers.

Clarification: $$a^n - b^n$$ must be an integer for all natural values of $$n$$, not just a few values of $$n$$.

×