Quadratic Reciprocity Theorem: Difference between revisions
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<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> | ||
*Note that <math>\left(\frac{p}{q}\right)</math> is not a fraction. It is the Legendre notation of quadratic residuary. | |||
==See Also== | ==See Also== | ||
[[Category:Number theory]] | [[Category:Number theory]] | ||
[[Category:Theorems]] | [[Category:Theorems]] | ||
[[Quadratic Residues |Quadratic Residues]] | |||
Latest revision as of 22:21, 5 April 2021
Quadratic reciprocity is a classic result of number theory.
It is one of the most important theorems in the study of quadratic residues.
Statement
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:
- Note that
is not a fraction. It is the Legendre notation of quadratic residuary.
is not a fraction. It is the Legendre notation of quadratic residuary.
