jmc

When working modulo $m$, the notation $a^{-1}$ is used to denote the residue $b$ for which $ab\equiv 1(\mathrm{mod}m)$, if any exists. For how many integers $a$ satisfying $0\le a<100$ is it true that $a(a-1{)}^{-1}\equiv 4a^{-1}(\mathrm{mod}20)$?