Ok, so is an integer iff (I'm guessing p is a fixed prime number...), so we can say that if , then:
, so if we also have and assuming the quotient group's unit (i.e., ), then
(note that it must be as well! (why??).
Now, if , then we'd get that , as , but this can't be since ...!
So it must be . Q.E.D.