Prove the following more general version of the Chinese
Remainder Theorem: Theorem. Let m1, . . . , mN ∈ N, and let M =
lcm(m1, . . . , mN ) be their least common multiple. Let a1, . . .
, aN ∈ Z, and consider the system of simultaneous congruence
equations x ≡ a1 mod m1 . . . x ≡ aN mod mN This system
is solvable for x ∈ Z if and...