Timeline for Primitive roots
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Nov 15, 2022 at 9:59 | comment | added | Martin Brandenburg | I agree, the title should be changed. "Primitive roots" is not specific enough. | |
| Jan 28, 2011 at 4:05 | comment | added | Pete L. Clark | @Hej: although your question is quite clear, I think it's natural that people are misreading it (as you mentioned in a comment below). Namely, a primitive root mod p is a generator of (Z/pZ)^*, so it is natural to (mis)read your question as: "Are there infinitely many primes p such that 2 or 3 is a primitive root mod p?" especially if you know about the result of Heath-Brown which is "slightly weaker" than this. You are weakening APR in a somewhat unexpected direction by allowing more than one generator. (Anyway, good question!) | |
| Jan 28, 2011 at 3:00 | answer | added | Joe Silverman | timeline score: 13 | |
| Jan 28, 2011 at 2:55 | history | edited | Zev Chonoles |
changed tags
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| Jan 28, 2011 at 2:35 | comment | added | Zev Chonoles | Or indeed $\text{lcm}(j,k)<p-1$. But that would only be one counterexample - is there an intuitive reason why we should expect it to occur for all but finitely many primes? | |
| Jan 28, 2011 at 2:31 | comment | added | David Hansen | I am going to guess "probably not" - if you can find a prime $p$ and positive integers $j,k$ with $2^{j} \equiv 3^{k} \equiv 1 \, \mathrm{mod} \, p$ and $j*k < p-1$, then you've found a counterexample. | |
| Jan 28, 2011 at 2:12 | comment | added | Zev Chonoles | +1 by the way - neat question. | |
| Jan 28, 2011 at 2:07 | comment | added | Zev Chonoles | Hej, I've changed $\mathbb{Z}_p^*$ to $(\mathbb{Z}/p\mathbb{Z})^\times$, because the generally accepted meaning of $\mathbb{Z}_p$ is the $p$-adic integers (though I don't think anyone was confused about what you meant), and because after changing that aspect, the asterisks gave me trouble with the markdown. | |
| Jan 28, 2011 at 2:04 | history | edited | Zev Chonoles | CC BY-SA 2.5 |
changed Z_p to Z/pZ, removed some unnecessary words
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| Jan 28, 2011 at 2:01 | history | edited | Hej | CC BY-SA 2.5 |
clarification
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| Jan 28, 2011 at 1:50 | answer | added | GH from MO | timeline score: 18 | |
| Jan 28, 2011 at 1:22 | history | asked | Hej | CC BY-SA 2.5 |