I'm wondering if it's possible to find the public exponent ($e$) with an example and the (rather small) values of $p$ and $q$ given.
Currently the only option I found is bruteforcing this value, but this can be very slow for a large $e$.
And if there is no perfect technique, is there a way to limit the amount of options significantly?
Is it possible to find $e$ with $p$, $q$ and an example encrypted message + answer given?