Given an initial number $m$ and a modulo $n$, is there a way of determining some constant multiplier $k$ so that $(m \times k^x) \mod n$ will eventually yield all integers in $[1,n]$ by incrementing $x$?
Alternately, if I instead do $(m \times x) \mod n$ while incrementing $x$ every step, will that eventually yield every integer in $[1,n]$?