Show by any method of construction that the language $A = \{a^i b^j\}$ is regular.
restrictions:
1) $i$ is a multiple of any given integer $n$
2) $j$ is a multiple of any given integer $m$
3) $n,m \geq 0$
I tried to prove this by cases. Having a case where n is even and a case where n is odd. And the same cases for m. But I didn't make it very far with this. I am not well versed in proving this type of problem and would appreciate it if someone could give a me a direction to move in. I hope the description of the problem is clear enough if not let me know.