How can I prove that this language isn't regular using the pumping lemma for regular language?$$L = \{a^nb^m| n,m > 0, \gcd(n,m)=1\}$$I've already checked this answer: Proof that a language involving $gcd$ is not context-free but don't understand this part.Let s' be $a^{(n+ik)}b^m \ with \ k \geq 1$. Then s' e L if $gcd(n + ik, m) =$ , however the modular equation $n+ik = 0(m)$ have a solution $i = nk^{(-1)(m)}$ ...I don't understand how he proved, $gcd(n+ik, m) \gt 1$, could someone explain me more clearly the answer please.Thank you.
Prove this langage isn't regular using the pumping lemma
formal languages;regular languages;pumping lemma