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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 $k\bmod q$?
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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
Oct 7, 2021 at 10:10
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.
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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.
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Oct 6, 2021 at 16:13 history closed Chris Wuthrich
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Alexey Ustinov
Daniele Tampieri
LeechLattice
Duplicate of Finding the square root modulo n, when the factors of n are known
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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