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.
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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.
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