hi everyone

anyone up for taking a look at these congruence proofs? ;3

5. (a) Prove that if p is a prime, then the only solutions of x^2 congruent to 1 (mod p) are integers x such that x congruent to 1 (mod p) or x congruent to −1 (mod p).

The quotient ring a prime, is in fact a field, and thus any polynomial with coefficients in it has at most of the polynomial different roots, so
(b) Suppose that p is not a prime. Then does the statement stay valid, i.e., the only solutions of x^2 congruent to 1 (mod p) are integers x such that x congruent to 1 (mod p) or x congruent to −1 (mod p). Give a

proof or a counterexample.

Count how many elements are there in which fulfill Tonio