Cofactor Cofantasy

We can factor $N$ using the given phi, or just simply look up the number on FactorDB. If the number returned has the form of $c = g ^ {k}$ with some even number $k$, we have the observation that for every factor of $N$, $c$ is a quadratic residue under that base, whereas the randomly generated number almost never generate a number that is a quadratic residue of all factors....