A12183 | Div Times Mod

The result of integer division $a~\mathrm{div}~b$ is equal to the largest integer $c$ such that $b \cdot c \leq a$ . $a$ modulo $b$ (shortened $a \bmod b$ ) is the only integer $c$ such that $0 \leq c < b$ , and $a - c$ is divisible by $b$ .

In the first sample, $11~\mathrm{div}~3 = 3$ and $11 \bmod 3 = 2$ . Since $3 \cdot 2 = 6$ , then $x = 11$ is a solution to $(x~\mathrm{div}~3) \cdot (x \bmod 3) = 6$ . One can see that $19$ is the only other positive integer solution, hence $11$ is the smallest one.