Let p be a prime, let K be a number not divisible by p, and let b be a number that has a kth root modulo p.

Let p be a prime, let K be a number not divisible by p, and let b be a number that has a kth root modulo p. Find a formula for the number of kth roots of b modulo p and prove that your formula is correct. (hint. your formula should only depend on p and k, not on b.)