Show that ifpis a prime andp=2q+1, whereqis an odd prime andais a positive integer with 1 < a < p-1, then p- is a primitive root modulop.

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- Nov 3rd 2010, 10:27 PMJanu42Primitive Root Question
Show that if

*p*is a prime and*p=2q+1*, where*q*is an odd prime and*a*is a positive integer with 1 < a < p-1, then p- is a primitive root modulo*p*. - Nov 11th 2010, 12:17 PMPaulRS
Note that what does this tell you about ? and about ?

Next, prove that all non-quadratic residues module p (except for -1) must be primitive roots module .

Hint : Count

Link the two parts.