[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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