Let p = 2^(k) + 1 be a prime. Prove that if a is a natural number and a is a quadratic non-residue modulo p, then a is a primitive root modulo p. thanks
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Originally Posted by Tand Let p = 2^(k) + 1 be a prime. Prove that if a is a natural number and a is a quadratic non-residue modulo p, then a is a primitive root modulo p. thanks Euler's Criterion says But , so we know . Now all the divisors of are of the form where . So suppose there exists such that . This would however imply since , which is a contradiction. Thus we see for every proper divisor of , is a primitive root modulo .
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