Question

Let a and b be any integer, if a|b then a^2|b^2. True or false?

Answer 1

If 2|4 then does 4|16 yes.. answers are 2 and 4
If 15|30 then does 225|900 answers are 2 and 4

If you think of 15 as 3 times 5 then squared gives you 3355
if you think of 30 as 2 times 3 times 5 then squared gives you 223355
Everything cancels except the 2 times 2 which is 4.

Answer 2

True
if a|b then b = ka for some integer k
b^2 = (ka)^2 = k^2 a^2 which is a multiple of a^2