# Playing In The Gaussian Plane

$\large z^{120}\equiv 1\pmod{8+3i}$

How many (incongruent) solutions $$z=a+bi$$ does the congruency above have among the Gaussian integers $$z$$?

Recall that $$z_1\equiv z_2\pmod{8+3i}$$ if $$z_1-z_2=(8+3i)w$$ for some Gaussian integer $$w$$.

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