# It's all about number theory! (1)

**Number Theory**Level 4

\[\begin{cases} ab+a+b = 524\\ bc+b+c = 146 \\ cd+c+d = 104 \end{cases} \]

The product of four positive integers \(a\), \(b\), \(c\), and \(d\) is \(8! \). If these numbers satisfy the system of equations above, find the value of \(a-d\).