let be a proper subgroup of then there exists an integer such that let then for all and
in here i showed that for all integers coprime with and for all therefore:
Let p be a prime and let .
Prove that the only proper subgroups of are the finite cylic groups
Proof so far.
Suppose to the contrary that H is a subgroup of such that and . Now, suppose that , then . But how would I get a contradiction? Thanks.