# Euler gone wild, one last time

$\large a^{9074}\equiv{a^2}\pmod{19845}$

How many integers $$a$$ with $$1\leq{a}\leq1000$$ satisfy the congruency above?

Extra Credit Question: How many integers $$a$$ with $$1\leq{a}\leq1000$$ satisfy the congruency $\large a^{758}\equiv{a^2}\pmod{19845}$

Inspiration here, here, and here.

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