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> |
| − | \left(\frac{p}{q}\right)\left(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}} | + | <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.<\br> 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:<\br>
