Question 100
Find all nonzero natural numbers $a$, $b$ and $c$ for which there exist nonzero natural numbers $x$, $y$ and $z$ such that $x! = a b + 1$, $y! = b c + 1$ and $z! = c a + 1$.
Remark: For every nonzero natural number $n$, the integer $n!$ denotes the product $1 \times 2 \times \cdots \times n$.
Remark: For every nonzero natural number $n$, the integer $n!$ denotes the product $1 \times 2 \times \cdots \times n$.