##  [Law of Quadratic Reciprocity](/law-quadratic-reciprocity) 

  ##  [Law of Quadratic Reciprocity](https://puremath.quantumdictionary.io/law-quadratic-reciprocity-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A fundamental result in elementary number theory that relates quadratic residuosity between two distinct odd primes p and q via the Legendre symbol: (p/q)(q/p) = (-1)^{((p-1)/2)((q-1)/2)}; it determines whether p is a quadratic residue modulo q in terms of the reverse question up to an explicit sign.