Proofs if a divides b then a3 divides b3Solutiona divides b

Proofs:

if a divides b then a^3 divides b^3

Solution

a divides b.

This implies b/a = k for some integer k.

=> b = ak

=> b³ = k³ a³

=> b³/a³ = k³ for some integer k³

Hence, a^3 divides b^3.

Therefore, if a divides b then a^3 divides b^3