IMO 1983 - Shortlisted problems Question 18

(FRG 3) IMO3. Let $a,b,c$ be positive integers satisfying $(a,b)=(b,c)=(c,a)=1$. Show that $2abc-ab-bc-ca$ is the largest integer not representable as
$$xbc+yca+zab$$
with nonnegative integers $x,y,z$.