Let
![a,b](/media/m/7/d/8/7d8bdace47e602448e6040957d8cf923.png)
and
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
be positive integers, no two of which have a common divisor greater than
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
. Show that
![2abc-ab-bc-ca](/media/m/0/5/c/05ca56ddd47c9ca786517373e5dde3f7.png)
is the largest integer which cannot be expressed in the form
![xbc+yca+zab](/media/m/d/1/2/d1258d30e0291e3197f328767ca1ab55.png)
, where
![x,y,z](/media/m/b/7/2/b72c022e9d438802d328d34eb61bb4ba.png)
are non-negative integers.
%V0
Let $a,b$ and $c$ be positive integers, no two of which have a common divisor greater than $1$. Show that $2abc-ab-bc-ca$ is the largest integer which cannot be expressed in the form $xbc+yca+zab$, where $x,y,z$ are non-negative integers.