##  [Pell's Equation Principle](/pells-equation-principle) 

  ##  [Pell's Equation Principle](https://puremath.quantumdictionary.io/pells-equation-principle-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The body of results describing integer solutions of the Pell equation x^2 − D y^2 = 1 for nonsquare positive integers D, notably that solvability is equivalent to the existence of units of norm ±1 in the real quadratic field Q(√D) and that a fundamental solution generates an infinite sequence of solutions via powers of a fundamental unit.