I can solve normal modulo questions but am having a bit of trouble with this question if anybody could help that would be grateful.
Suppose $(a,m)=1 $ For all $a$ prove that the solution of $ax\equiv 1\pmod{m^s}$
is $x\equiv k \pmod{m^s}$ where $k$ is the nearest integer to $ −(1/a)(1 − ax1)^s$