Checking if a Language is Regular

Question

When asked to prove the Language is regular, where do you start?

What methods do we have to prove this Language is regular?

Language {a^n | n<>2 and n<>≡ 3(mod 7)}

Answer 1

As a hint: if you make a cycle of 7 states linked in a ring and number them 0, 1, 2, 3, ..., 6, what can you say about any string w that ends up in state number k? Based on that, could you make some of these states accepting to get the language you want?

Hope this helps!