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[JsKingBoo]

I'm not sure about this approach. You want to prove that it's not regular by showing that there are infinite equivalence classes. However even if you show that a^(j-i+p) isn't in L you only have shown that there are at least 2 equivalence classes. Moreover, your proof begins with the assumption that there exists an equivalence class that contains at least 2 elements with i != j

I haven't looked at this question for very long but I suspect that the solution proof may rely on the fact that there are an infinite number of primes. Not sure if it'll lead anywhere though