Math.NumberTheory.Pell

This module provides a function to solve generalized Pell Equations, using the "LMM Algorithm" described by John P. Robertson in http://www.jpr2718.org/pell.pdf. A generalized Pell Equation is a diophantine equation of the form x^2 - dy^2 = n, where d is a positive integer which is not a square and where n is a non-zero integer. We are looking for solutions (x,y), where x and y are non-negative integers.

Documentation

type Solution = (Integer, Integer)

Represents a solution to a generalized Pell Equation. The first component is the value of x, the second component that of y.

solve :: Integer -> Integer -> [Solution]

solve d n calculates all non-negative integer solutions of the generalized Pell Equation x^2 - dy^2 = n, where d must be a positive integer which is not a square, and n must be a non-zero integer.