Timeline for Method to solve modular quadratic polynomial [duplicate]
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Oct 7, 2021 at 19:25 | comment | added | Turbo | @ChrisWuthrich Can you tell me the name for the technique? So I can look it up? | |
Oct 7, 2021 at 10:34 | comment | added | Turbo | @ChrisWuthrich Oh I see. Is it just substituting symbol for root as $-b+kq$ in the quadratic and solving for $k\bmod q$? | |
Oct 7, 2021 at 10:14 | history | undeleted | Turbo | ||
Oct 7, 2021 at 10:13 | history | deleted | Turbo | via Vote | |
Oct 7, 2021 at 10:10 | history | left closed in review |
Alex M. Alexey Ustinov Emil Jeřábek |
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Oct 7, 2021 at 9:18 | history | edited | Turbo |
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S Oct 7, 2021 at 8:09 | review | Reopen votes | |||
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S Oct 7, 2021 at 8:09 | history | edited | Turbo |
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Oct 7, 2021 at 7:54 | comment | added | Chris Wuthrich | Yes, I am answering the additional question with $q^2\mid \Delta$. It is an easy extension of the methods described in the linked answer and does not vouch for reopening the question. I won't have time to explain $p$-adic numbers, so please read up on them and how to find square roots there; it is fun. | |
Oct 7, 2021 at 7:48 | comment | added | Turbo | $p^2|discriminant$ not just $p$ as you mention. | |
Oct 7, 2021 at 7:46 | history | edited | Turbo | CC BY-SA 4.0 |
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Oct 7, 2021 at 7:41 | comment | added | Turbo | So can you explain the answer explicitly for computational number theory purposes? I believe the problem is not exact duplicate. So perhaps reopenable? So is root mod $q^2$ computable in polynomial time? Is there a reference to what you are talking about? $b$ and $q$ may be assumed coprime. | |
Oct 7, 2021 at 7:40 | history | edited | Turbo | CC BY-SA 4.0 |
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Oct 7, 2021 at 7:40 | comment | added | Chris Wuthrich | $\mathbb{Q}_p$ is the field of $p$-adic numbers. I don't think your question is asked at the right forum. | |
Oct 7, 2021 at 7:38 | comment | added | Chris Wuthrich | After edit: The case when $p$ divides the discriminant isn't harder. To find the square root in $\mathbb{Q}_p$ the valuation has to be even and then use Hensel's lemma on the unit part. Which by the way is the usual algorithm $x \to 1/2(x+a/x)$ to find square roots. | |
Oct 7, 2021 at 7:28 | history | edited | Turbo | CC BY-SA 4.0 |
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Oct 7, 2021 at 5:45 | history | edited | Turbo | CC BY-SA 4.0 |
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Oct 6, 2021 at 16:13 | history | closed |
Chris Wuthrich user44191 Alexey Ustinov Daniele Tampieri LeechLattice |
Duplicate of Finding the square root modulo n, when the factors of n are known | |
Oct 6, 2021 at 4:21 | review | Close votes | |||
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Oct 6, 2021 at 4:19 | history | undeleted | Turbo | ||
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Oct 5, 2021 at 8:38 | comment | added | Chris Wuthrich | ... which links to mathoverflow.net/questions/52081 | |
Oct 5, 2021 at 8:30 | comment | added | Chris Wuthrich | mathoverflow.net/questions/54936 is a duplicate | |
Oct 5, 2021 at 8:24 | answer | added | Peter Taylor | timeline score: 0 | |
Oct 5, 2021 at 7:40 | history | asked | Turbo | CC BY-SA 4.0 |