Show that relative primality was mandatory for the Chinese Remainder Theorem. Namely, show that, for two integers n and m that are not necessarily relatively prime, for some a ∈ Zn and b ∈ Zm . . . 1....

Show that relative primality was mandatory for the Chinese Remainder Theorem. Namely, show that, for two integers n and m that are not necessarily relatively prime, for some a ∈ Zn and b ∈ Zm . . .

1. . . it may be the case that no x ∈ Znm satisfies x mod n = a and x mod m = b.

2. . . it may be the case that more than one x ∈ Znm satisfies x mod n = a and x mod m = b