Letrbe a primitive root of the primepwith p congruent to 1 (mod 4). Show that -r is also a primitive root.

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- October 27th 2010, 08:55 PMJanu42Primitive Root Question
Let

*r*be a primitive root of the prime*p*with p congruent to 1 (mod 4). Show that -r is also a primitive root. - October 28th 2010, 01:54 AMPaulRS
Note that since and so -since p is prime- or , but the former is not possible since r is a primitive root.

Thus so your problem is equivalent to showing that is coprime to .

But and so is either 1 or 2.

Now note that 4 doesn't divide p+1, since p-1 is divisible by 4, and so (p+1)/2 must be odd. - March 22nd 2013, 03:33 AMuserit8Re: Primitive Root Question