Seems to me like you copy-pasted your assignment problem.
Let n be a natural number. Determine the set of prime numbers p such
that −1 is a n-th power modulo p.(that is, such that there exists an integer
a^n such that an −1 (mod p)).
(Hint: the case n = 1 is trivial, and we have
done the case n = 2 in class. What can you say in the case n odd? and in
the case where n is a power of 2? Then we can get the general case).