Talk:Quadratic reciprocity

message: Dear DYLAN LENNON,
Could you please explain how you intend to use quadratic reciprocity to prove fermat's theorem on sums of two squares. The only part that I can see is vaguely relevant is the first supplementary theorem, i.e. that \left(\frac{-1}p\right) = (-1)^{(p-1)/2}, which is by far the most trivial part of QR. (I have taken the liberty of reverting your edit again until you can provide an explanation.) Dmharvey 01:53, 5 February 2006 (UTC)
replies: text: I've had a look, and I can't find what you mean. Could you give a page number perhaps? Even better, which paragraph/sentence supports your claim? Dmharvey 02:50, 5 February 2006 (UTC)
thread_title: comment on Fermat's theorem

message: Is there a further formulation of reciprocity?? let's say an study of the solutions:
 x^{n}=p mod (q)    x^{n}=q mod (p)  —The preceding unsigned comment was added by 85.85.100.144 (talk) 21:01, 19 February 2007 (UTC)
thread_title:  n-th reciprocity

message: I started trying to make a table of residues to illustrate quadratic reciprocity, but it soon got very painful to do by hand. So I wrote a Python script (my first!) to do it for me. Of course, just editing the script here won't update the table, you'll have to run it on your own machine :-)

    # find primes from 3 up to max
    max = 50
    primes = []
    for n in range(3, max):
        composite = False
        for d in range(2, n-1):
            if n % d == 0:
                composite = True
                break
        if not composite:
            primes.append(n)
            
    count = len(primes)
    yes_marker = '✓'   # tick (U.S. "check") for residues
    no_marker  = '✗'   # cross for non-residues
    def colortag(n):
        if n % 4 == 1:
            return 'bgcolor=#e0ffff'
        else:
            return 'bgcolor=#ffe0e0'
    # computes Legendre symbol (a/q)
    # assumes a and q positive, q prime, (a, q) = 1
    def legendre(a, q):
        for n in range(1, q-1):
            if (n * n) % q == a % q:
                return 1;
        return -1;
        
    # print table header
    print '{| class="wikitable"'
    print '|-'
    print '| || colspan=' + str(count+1), 'align="center" |', "p"
    print '|-'
    print '| rowspan=' + str(count+1), "|  q  || ",
    for p in primes:
        print '||', colortag(p), 'align="center" style="border-bottom:2px solid" |', "" + str(p) + "", 
    print
    # now the main table
    for q in primes:
        # first column
        print '|-'
        print '|', colortag(q), 'align="right" style="border-right:2px solid" |', " " + str(q) + " ",
        # remaining columns
        for p in primes:
            print '||', colortag(1+(p-1)*(q-1)/2), '|',
            if p == q:
                print ' ',
            else:
                # symbol for (p/q)
                if legendre(p, q) == 1:
                    print yes_marker,
                else:
                    print no_marker,
                if legendre(q, p) == 1:
                    print yes_marker,
                else:
                    print no_marker,
        print
            
    print '|}'

Dmharvey 03:22, 21 April 2006 (UTC)
thread_title:  Python code for residue table 

message: Something's wrong with the chart... the check and cross marks both look like boxes.
63.228.45.224 16:23, 28 May 2007 (UTC)
thread_title:  Chart 

message: I will add a brief history section soon. User:Virginia-American/Sandbox
has changes for the article on quadratic residues. I don't anticipate anything so extensive here.
 
How about FAQ's
Why did CFG do so many proofs?
Why has everyone else as well?
Why "law" (it's not a thing like other laws, eg. commutative law of addition)?
Virginia-American (talk) 01:05, 28 February 2008 (UTC)
thread_title:  history section 

message: I colorized one of the tables and put the border back around it. Anyone have ideas for inproving the aesthetics of this? thanks Virginia-American (talk) 02:52, 12 November 2008 (UTC)
thread_title: Colors

message: This article is very nice and has a lot of good content, but the beginning reads more like an exposition than an encyclopedia article.  There needs to be statement of the full theorem (or at least one version of the theorem) much earlier in the article, ideally in the introduction or near the beginning of the first section.  The tables of numbers and such are helpful for motivation and understanding, but they ought to be put in a "Motivation" section that occurs after the statement of the law. Jim (talk) 20:25, 23 November 2008 (UTC)
replies: text: done Virginia-American (talk) 14:28, 24 November 2008 (UTC)
thread_title:  Comments 

message: "A number of proofs of the theorem, especially those based on Gauss sums derive this formula.[20] or the splitting of primes in algebraic number fields,[21]"
Description in one word: Ungrammatical.  — Preceding unsigned comment added by 189.63.168.238 (talk) 01:45, 16 April 2016 (UTC)
thread_title:  Problem 

message: Hello fellow Wikipedians,
I have just modified  on Quadratic reciprocity. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive http://web.archive.org/web/20120122104607/http://www.math.duke.edu/langlands/Three.pdf to http://www.math.duke.edu/langlands/Three.pdf
*Added archive http://web.archive.org/web/20070119103757/http://planetmath.org:80/encyclopedia/ProofOfQuadraticReciprocityRule.html to http://planetmath.org/encyclopedia/ProofOfQuadraticReciprocityRule.html
*Added  tag to http://www.mathpages.com/home/kmath075/kmath075.htm
When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).
Cheers.—InternetArchiveBot (Report bug) 12:10, 21 July 2016 (UTC)
thread_title:  External links modified