In: Advanced Math
Determine whether each of the following statements is True or False. If True, write a proof. If False, exhibit a counterexample.
1) If m, n are arbitrary positive integers, then any system of form
x ≡ a (mod m)
x ≡ b (mod n)
has a solution.
2) If m, n are arbitrary positive integers and the system
x ≡ a (mod m)
x ≡ b (mod n)
has a solution, then the solution is unique modulo mn.
Modern Abstract Algebra