- #1

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- 6

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Determine a primitive root modulo 19, and use it to find all the primitive roots.

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[tex]\varphi(19)= 18[/tex]

And 18 is the order of 2 modulo 19, so 2 is a primitive root modulo 19, but I am not sure of how to use that to find all primitive roots modulo 19. My only idea is that we need to find what values of g satisfy [itex]g^{18} \equiv 1 \ \text{mod 19}[/itex]. However, I am not sure how to solve that equation. Any ideas? Thanks!