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that there can be at most $p − 1$ consecutive positive integers coprime to $n$.

b) Show further that the number $p − 1$ in (a) cannot be decreased, by exhibiting

$p − 1$ consecutive positive integers coprime $n$.

c) What is gcd$(p − 1, n)$?

d)Show that $2^n \not\equiv 1 (mod n)$.

I think the first part has something to with the fact that two positive integers are coprime iff they have no prime factors in common. As if there were more than $p-1$ consecutive numbers then they would have a coprime in common. Not sure how to word this convincingly!!

Not sure for b). Guessing I'd say c) is $p-1$, though not sure. d).. no clue!

If you can point me in the right direction I'd appreciate it, thanks.