Difference between revisions of "Talk:Quadratic residues"
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I'm sure someone wants to write out all the fun properties of Legendre symbols. It just happens not to be me right now. -- ComplexZeta | I'm sure someone wants to write out all the fun properties of Legendre symbols. It just happens not to be me right now. -- ComplexZeta | ||
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| + | Is it any number n, or any integer n? --- cosinator | ||
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| + | Where? --[[User:ComplexZeta|ComplexZeta]] 11:07, 27 June 2006 (EDT) | ||
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| + | In the introduction it says 'We say that a is a quadratic residue modulo m if there is some number n so that n^2 − a is divisible by m.' | ||
| + | If it were any number, I would think that any a could be a quadratic residue modulo m | ||
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| + | Thanks for clarifying -Cosinator | ||
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| + | ''Whereas the above are properties of the Legendre symbol, they still hold for any odd integers p and q when using the Jacobi symbol defined below''. | ||
| + | Hmmm... The quadratic reciprocity law clearly fails (at least in the form as written for primes) if <math>\gcd(m,n)>1</math>. So some correction is needed. My knowledge of number theory really needs some refreshment, so could someone else write the correct statement here? --[[User:Fedja|Fedja]] 14:34, 28 June 2006 (EDT) | ||
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| + | Yes, coprime was missing. | ||
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| + | Rather than having this page link to a seperate page for the Legendre symbol, wouldn't it make more sense to just have the Legendre symbol page be a redirect here? (After all, there isn't anything to say about the L. symbol that doesn't say things about q. residues.)--[[User:JBL|JBL]] 10:01, 13 July 2006 (EDT) | ||
Latest revision as of 09:01, 13 July 2006
I'm sure someone wants to write out all the fun properties of Legendre symbols. It just happens not to be me right now. -- ComplexZeta
Is it any number n, or any integer n? --- cosinator
Where? --ComplexZeta 11:07, 27 June 2006 (EDT)
In the introduction it says 'We say that a is a quadratic residue modulo m if there is some number n so that n^2 − a is divisible by m.' If it were any number, I would think that any a could be a quadratic residue modulo m
Thanks for clarifying -Cosinator
Whereas the above are properties of the Legendre symbol, they still hold for any odd integers p and q when using the Jacobi symbol defined below.
Hmmm... The quadratic reciprocity law clearly fails (at least in the form as written for primes) if 
. So some correction is needed. My knowledge of number theory really needs some refreshment, so could someone else write the correct statement here? --Fedja 14:34, 28 June 2006 (EDT)
Yes, coprime was missing.
Rather than having this page link to a seperate page for the Legendre symbol, wouldn't it make more sense to just have the Legendre symbol page be a redirect here? (After all, there isn't anything to say about the L. symbol that doesn't say things about q. residues.)--JBL 10:01, 13 July 2006 (EDT)
