# Primitive roots are magic

$\displaystyle \left( \prod _{\text{ord}(n)<p-1}^{}{ n } \right) \pmod{1601}$

Consider the prime number $$1601$$. Let $$\text{ord}(x)$$ denote the least $$j>0$$ such that $$x^j\equiv 1 \pmod{1601}$$. Evaluate the product above over the set of nonzero residues modulo $$1601$$.

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