Thread: Prime # Proof

Let a, b, c, and d be natural numbers. Show that if ab = cd, then a² + b² + c² + d² is not prime. Generalize.

Originally Posted by MATNTRNG

Let a, b, c, and d be natural numbers. Show that if ab = cd, then a² + b² + c² + d² is not prime. Generalize.

I think the start goes like this:

$\displaystyle a^2+b^2+c^2+d^2$

$\displaystyle =a^2+2ab+b^2+c^2-2cd+d^2$

$\displaystyle =(a+b)^2+(c-d)^2$