Prove a relation is transitive

Question

I've stumbled upon this question in my discrete math book:

Prove

$$ R = \{(x,y) \in N \times N \ | \ 2x \mid y^2 \} $$

is transitive.

I tried thinking about it having to do something with division by 4 but couldn't proceed from there.

This is a question from really early stages of university studies so I think the solution should be mostly (if not entirely) algebraic.

Thanks!

Answer 1

This is not transitive because $(32, 8) , (8,4) \in R$ but $(32,4) \notin R$.