1. The number of non-negative integer pairs $(a, b)$ that satisfy $|a-b|+a b=1$ is
(A) 1 ;
(B) 2 ;
(C) 3 ;
(D) 4 .
1.. (C)

Solution: $\left\{\begin{array}{l}|a-b|=1 \\ a b=0\end{array} \Rightarrow(1,0),(0,1)\right.$.
Also, $\left\{\begin{array}{l}|a-b|=0 \\ a b=1\end{array} \Rightarrow(1,1)\right.$.
$\therefore$ There are 3 pairs in total.