IMO 2001 Q6

Let $a$, $b$, $c$, $d$ be integers with $a>b>c>d>0$. Suppose that

$$a\ast c+b\ast d=(a+b-c+d)\ast (-a+b+c+d).$$

Prove that $a\ast b+c\ast d$ is not prime.

theorem imo2001_q6 {a b c d : ℤ} (hd : 0 < d) (hdc : d < c) (hcb : c < b) (hba : b < a) (h : a * c + b * d = (a + b - c + d) * (-a + b + c + d)) : ¬Prime (a * b + c * d)