## proof of fermat's divisibilty examination problem?

hello.
there is a problem :

suppose b is member of N (Natural Numbers) and q is prime number that doesn't divide b . proof that there is n member of N (Natural Numbers) that $n|(q-1)$ and $q|(b^{(q-1)/n}-1)$

How to proof this problem?
can any one proof that please?
any help appreciated.