* $a, b, c, d$ are pairwise distinct positive integers, and $a+b=c d, a b=c+d$. Find all quadruples $(a, b, c, d)$ that satisfy the above requirements.
Assume without loss of generality that among $a, b, c, d$, $a$ is the smallest. From the given,
$$
a b-(a+b)=(c+d)-c d .
$$

This can be rewritten as $(a-1)(b-1)=2-(c-1)(d-1)$.
If $a \geqslant 2$, then $c, d$ are both greater than 2. The left side $\geqslant 0$, while the right side $<0$. Therefore, it must be that $a=1$. Additionally, $c=2$, $d=3$ or $c=3, d=2$. Thus, $b=5$.

Therefore, the tuples $(a, b, c, d)$ that satisfy the condition are: $(1,5,3,2),(1,5,2,3),(5,1,3,2)$, $(5,1,2,3),(2,3,1,5),(3,2,1,5),(2,3,5,1),(3,2,5,1)$.