If i have the following values
$(1) m\prime=(r^e.m) \% n$
$(2) s\prime=(r.m^d) \% n$
If i have access to the value of $m$,$d$, $m^d$,$m\prime$,$s\prime$,$n$,$p=11$,$q=19$, $\phi=(p-1)(q-1)=180,$ and $e$. Is it possible to get the value of $r$, if yes what is the best way to do it?
Numeric example: $r=13$, $e=7$, $n=209$, $m=16$,$d=103$,
$m\prime= (r^e.m)\%n = (13^7 .16)\%209 =46$
$s\prime=(r.m^d) \% n=(13.16^{103}) \% 209 = 8$