COMPUTATIONAL NUMBER THEORY
1. For every positive integer b, show that there exists a positive integer n such that the polynomial x^2 − 1 ∈ (Z/nZ)[x] has at least b roots.
2. Suppose n is a positive integer and there exists a primitive root modulo n. Prove that the only solutions to x^2 ≡ 1 (mod n) are x ≡ 1 (mod n) and x ≡ −1 (mod n).