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Mathematics

Primitive Root Modulo n

Quick fact

A primitive root modulo n exists only for n = 2, 4, p^k, or 2p^k (for odd prime p), a result proven by Gauss. For example, 3 is a primitive root modulo 7 because its powers cycle through all six nonzero residues.

Why this is interesting

Imagine a clock where instead of adding hours, you multiply numbers, and one special number can spin through every other hour. What is that magical number, and when does it exist?