Show that the number $122^n - 102^n - 21^n$ is always one less than a multiple of $2020$, for any positive integer $n$.
Source: New Zealand MO 2019 Round 1 p4
Tags: number theory, divides, divisible, multiple
Show that the number $122^n - 102^n - 21^n$ is always one less than a multiple of $2020$, for any positive integer $n$.