Without using a calculator determine the least non-negative residue $x$ such that
$$ 96 × 97 × 98 × 99 × 100 \equiv x \pmod {101} $$
We proceed as follows
$$ \begin{align} 96 \times 97 \times 98 \times 100 & \equiv (-5) \times (-4) \times (-3) \times (-2) \times (-1) \pmod {101} \\ \\ & \equiv -120 \pmod {101} \\ \\ & \equiv 82 \pmod {101} \end{align} $$
The least non-negative residue is $x=82$.