I would like to find small $b$ such that $$ b^e\equiv1\pmod m $$ for a given $e$ and $m$. (In my application, $m$ is the square of a prime.) How can I find such $b$? (Say, the first 10 or 100.)
I'm interested in something practical for $e$ with 10-20 digits and $m$ with 20-40 digits.
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