(the quadratic reciprocity theorem), of which Gauss gave the first correct proof. ... In the 1920s, Artin formulated Artin's reciprocity theorem, ...
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mathworld.wolfram.com/ReciprocityTheorem.html
mathworld.wolfram.com/ReciprocityTheorem.html
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of the Law of Quadratic Reciprocity: for distmct odd primes p and q, the congruences x .... results have been formulated and verified by the theorem prover. ...
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www.springerlink.com/index/K117360H53611K62.pdf
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Godel's Theorem. The proof, published by Kurt Godel in 1931, of the existence of formally undecidable propositions in any formal system of arithmetic. ... …The fact that the first incompleteness proof can be formalized in S allows one to derive Godel's second incompleteness theorem as a corollary. This theorem states...
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www.faragher.freeserve.co.uk/godeldef2.htm
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He formulated prime number theorem, which states that number of primes less than x is assimptotically ~x/logx. (error term is related to famous Riemann hypothesis which might have been recently proven); He published Disquisitiones Arithmeticae in 1801, which contained a his proof of quadratic reciprocity.
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The Quadratic Reciprocity Theorem compares the quadratic character of two primes with respect to each other. The quadratic character of q with respect to p is expressed by the Legendre symbol , defined to be 1 if q is a quadratic residue (i.e., a square) modulo p, and -1 if not.
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www.math.nmsu.edu/~history/schauspiel/schauspiel.html
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Quadratic reciprocity - Wikipedia, the free encyclopedia
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The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which gives conditions for the solvability of quadratic equations modulo prime numbers. There are a ...
en.wikipedia.org/wiki/Quadratic_reciprocity
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Theorem 1 (Law of Quadratic Reciprocity) Let $p$ and $q$ be two distinct odd primes. Then: ... Theorem 2 (Quadratic Reciprocity (second form)) Let $p,q$ be distinct odd primes. Then:
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planetmath.org/encyclopedia/QuadraticReciprocityRule.ht...
planetmath.org/encyclopedia/QuadraticReciprocityRule.html
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