# [seqfan] Re: Sequence A019334

David Wilson davidwwilson at comcast.net
Wed Jun 17 04:15:51 CEST 2009

```n is a primitive root of p if n generates all the nonzero residues modulo p.

In the case p = 2, the primitive root 1 generates all residues modulo 2. But so does 3 or any odd number, which are all congruent to 1 (mod 2).

In the general case, if r is a primitive root of prime p, then r+pk is also a primitive root of p.

In most treatments of primitive roots of p, the context is modulo p arithmetic, so primitive roots of p are generally considered residues modulo p, which are expressed by numbers less than p. If we honor that convention, 3 would not be considered a primitive root of 2.

So I will leave it to seqfan (Neil) as to whether values >= p should be considered primitive roots of p with regard to the sequences in question.

----- Original Message -----
From: Harry J. Smith
To: davidwwilson at comcast.net
Sent: Tuesday, June 16, 2009 12:22 PM
Subject: Sequence A019334

David:

Why do you have 2 in Sequence A019334, Primes with primitive root 3?

The prime number 2 has 1 primitive root equal to 1.

I have the same question about A019335, A019337, A019339, ., A019421

-Harry

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