Difference between revisions of "Quadratic Reciprocity Theorem"
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| − | Quadratic reciprocity is a classic result of number theory.< | + | Quadratic reciprocity is a classic result of number theory.<br> |
It is one of the most important theorems in the study of quadratic residues. | It is one of the most important theorems in the study of quadratic residues. | ||
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If both <math>p</math> and <math>q</math> are of the form <math>4n+3</math>, then <math>\left(\frac{p}{q}\right)= -\left(\frac{q}{p}\right)</math> | If both <math>p</math> and <math>q</math> are of the form <math>4n+3</math>, then <math>\left(\frac{p}{q}\right)= -\left(\frac{q}{p}\right)</math> | ||
| − | Another way to state this is:< | + | Another way to state this is:<br> |
<math>\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}</math> | <math>\left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}</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:
