Difference between revisions of "Quadratic Reciprocity Theorem"
Baijiangchen (talk | contribs) (Created page with "Quadratic reciprocity is a classic result of number theory. It is one of the most important theorem's in the study of quadratic residues. It states that <math>\left(\frac{p}{q}\...") |
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Quadratic reciprocity is a classic result of number theory. | Quadratic reciprocity is a classic result of number theory. | ||
− | It is one of the most important | + | It is one of the most important theorems in the study of quadratic residues. |
It states that <math>\left(\frac{p}{q}\right)= \left(\frac{q}{p}\right)</math> for primes <math>p</math> and <math>q</math> greater than <math>2</math> where both are not of the form <math>4n+3</math> for some integer <math>n</math>. | It states that <math>\left(\frac{p}{q}\right)= \left(\frac{q}{p}\right)</math> for primes <math>p</math> and <math>q</math> greater than <math>2</math> where both are not of the form <math>4n+3</math> for some integer <math>n</math>. |
Revision as of 20:53, 10 October 2011
Quadratic reciprocity is a classic result of number theory. It is one of the most important theorems in the study of quadratic residues.
It states that for primes and greater than where both are not of the form for some integer . If both and are of the form , then
Another way to state this is: \left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}