Question

Show that if a ≡ b (mod n) and c is a positive integer, then ca ≡ cb (mod cn)

Answer 1

`a\equiv b\mod n` means there is some integer
`N` such that
`a=Nn+b`. Multiplying everything by
`c` gives
`ca=cNn+cb=N(cn)+cb`, which is the same as saying
`ca\equiv cb\mod cn`.