Question

Show that if a ≡ b (mod n) and m divides n, then a ≡ b (mod m).

Answer 1

If
`a\equiv b\mod n`, then there is some integer
`N` such that
`a=Nn+b`. Because
`m|n`, it follows that
`m|Nn`, which means there is some integer
`M` such that
`a=Mm+b`, which is equivalent to the statement that
`a\equiv b\mod m`.