I have two questions involving mod m that I am struggling with and I was hoping someone could give me some tips on how to start and or complete them

1. if a = b(mod m) and a = b(mod n), prove a = b(mod mn), I know that m and n are relatively prime. So the greatest common divisor of m and n is 1

2. If x^2 = a^2 (mod p), prove x= a(mod p) or x = -a (mod p). Where p is a prime..