Let
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
,
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
,
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
,
![e](/media/m/1/6/f/16f8978af0f3c64c3eb112a539ba73dd.png)
,
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
be positive integers and let
![S = a+b+c+d+e+f](/media/m/3/c/b/3cb573a2c95155ddd39f6859850789b6.png)
.
Suppose that the number
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
divides
![abc+def](/media/m/8/3/b/83bd572cb0a03cd2c90263caa6e36697.png)
and
![ab+bc+ca-de-ef-df](/media/m/f/1/c/f1c8076d5c429cd59205256d19483812.png)
. Prove that
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
is composite.
%V0
Let $a$, $b$, $c$, $d$, $e$, $f$ be positive integers and let $S = a+b+c+d+e+f$.
Suppose that the number $S$ divides $abc+def$ and $ab+bc+ca-de-ef-df$. Prove that $S$ is composite.