We prove that for integers
a
>
b
>
c
>
0
a>b>c>0
, the greatest prime factor of
(
a
b
+
1
)
(
a
c
+
1
)
(ab+1)(ac+1)
tends to infinity with
a
a
. In particular, this settles a conjecture raised by Györy, Sarkozy and Stewart, predicting the same conclusion for the product
(
a
b
+
1
)
(
a
c
+
1
)
(
b
c
+
1
)
(ab+1)(ac+1)(bc+1)
.