555:# 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="db-d2lraXRhYmxl"' 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" |', "'''" + str(p) + "'''", print # now the main table for q in primes: # first column print '|-' print '|', colortag(q), 'align="right" |', "''' " + 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 '|}'
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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
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Does anyone know anything about this? Since the LS relation reduces to a Guass sum, and QR can be easily proved using Gauss sums, is this the extent of it, or is there more?
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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
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I changed the table to use images instead of
Unicode characters, as the Unicode characters don't show up on all computers (see previous comment). I put the new code on
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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 :-)
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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?
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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)?
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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
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I colorized one of the tables and put the border back around it. Anyone have ideas for inproving the aesthetics of this? thanks
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http://web.archive.org/web/20070119103757/http://planetmath.org:80/encyclopedia/ProofOfQuadraticReciprocityRule.html
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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341:. Use this, and Gauss's Law of Quadratic Reciprocity, to prove that 75 is a primitive root modulo 65537.
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774:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit
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yes_marker = ']' # tick (U.S. "check") for residues no_marker = ']' # cross for non-residues
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yes_marker = '✓' # tick (U.S. "check") for residues no_marker = '✗' # cross for non-residues
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has changes for the article on quadratic residues. I don't anticipate anything so extensive here.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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before doing mass systematic removals. This message is updated dynamically through the template
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http://web.archive.org/web/20120122104607/http://www.math.duke.edu/langlands/Three.pdf
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Is there a further formulation of reciprocity?? let's say an study of the solutions:
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Something's wrong with the chart... the check and cross marks both look like boxes.
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Could you please explain how you intend to use quadratic reciprocity to prove
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http://planetmath.org/encyclopedia/ProofOfQuadraticReciprocityRule.html
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page, it transpires that all I needed to do was to verify that
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When you have finished reviewing my changes, please set the
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for additional information. I made the following changes:
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http://www.math.nmsu.edu/~history/book/numbertheory.pdf
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