Question

Show that if 𝑎, 𝑏 𝑎𝑛𝑑 𝑐 are integers, where 𝑎 ≠ 0 and 𝑐 ≠ 0 such that 𝑎𝑐|𝑏𝑐, then 𝑎|𝑏.

Answer 1

ac|bc means that

bc = k*ac for some integer k.
Then
bc-k*ac = 0
c(b-ka) = 0
b-ka = 0
ka = b
a|b