Hello,

I wonder why make n = 2 x 7 = 14. Thank you.

If n = 14, notice that

504n

=504 \times 14

=(2^3 \times 3^2 \times 7) \times (2 \times 7)

=2^4 \times 3^2 \times 7^2

Can you see why that must be a perfect square?

Yes. Each number has to be even power to get the perfect square. Thank you.