Does there exist an integer
![z](/media/m/d/2/4/d241a79f1fdd0ce9a8f3f91570ba5d62.png)
that can be written in two different ways as
![z = x! + y!](/media/m/8/4/1/841dd129bd3d77e0cbe88e431147a20a.png)
, where
![x, y](/media/m/2/7/9/279a699b10f7b70e7160f4aaaa89e453.png)
are natural numbers with
![x \le y](/media/m/7/e/7/7e7869e827e930ac9555be520d0f3f0a.png)
?
%V0
Does there exist an integer $z$ that can be written in two different ways as $z = x! + y!$, where $x, y$ are natural numbers with $x \le y$ ?