If $a$ and $P$ are two relatively prime positive integers, such that
$a < P$, and $m$, $n$ are natural numbers less than $P$, will $(m*a)$ modulo $P$ ~= $(n*a)$ modulo $P$, always?
That is, will the multiples of $a$ modulo $P$, be not equal always? or will all the multiples of $a$ generate all the elements of the finite field GF(p). Note that P can be non-prime.