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Apr 1, 2018 at 20:14 comment added Fedor Petrov This seems to be a combinatorialization of Gauss sum proof, is not it? Counting these $q$-tuples is the same thing as taking the constant term of $q$-th power of the Gauss sum: $(\sum_{k=0}^{p-1} z^{k^2})^q$, where polynomials are taken modulo $z^p-1$.
Jul 10, 2013 at 14:07 history edited KConrad CC BY-SA 3.0
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S Jul 10, 2013 at 9:05 history suggested user22882 CC BY-SA 3.0
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Jul 10, 2013 at 8:52 comment added user22882 +1 I hope you find my TeXification acceptable. (Doing this is a good way to read a text more closely, by the way.)
Jul 10, 2013 at 8:50 review Suggested edits
S Jul 10, 2013 at 9:05
Jul 9, 2013 at 23:04 comment added Qiaochu Yuan Cool. If anyone's curious, I thought this was a really nice proof so I worked through the details as an exercise here: qchu.wordpress.com/2013/07/09/the-p-group-fixed-point-theorem
Jul 9, 2013 at 22:13 comment added KConrad @QiaochuYuan: Thanks, I made that fix to mod 8.
Jul 9, 2013 at 22:13 history edited KConrad CC BY-SA 3.0
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Jul 9, 2013 at 6:12 comment added Qiaochu Yuan For the supplementary law, when you say "the count mod p" do you mean "the count mod 8"?
Feb 9, 2010 at 19:20 comment added Franz Lemmermeyer A variant of this proof was recently given by W. Castryck, A shortened classical proof of the quadratic reciprocity law. Amer. Math. Monthly 115 (2008), 550-551
Jan 20, 2010 at 0:57 history edited KConrad CC BY-SA 2.5
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Jan 19, 2010 at 22:50 history answered KConrad CC BY-SA 2.5