]> Pell's Equation

Pell's Equation


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Definition

Pell's equation is defined as follows for natural numbers (x, y, N):

x 2 - N . y 2 = 1

It can be used to approximate irrational square roots by rational numbers. For more details, see:


Fundamental Solutions

The fundamental solutions to Pell's equation (also known as "minimal solutions") presented below were computed in 2012 using a Python program that implements the chakravala method (attributed to Bhaskara II). N is skipped if it is not square-free (i.e., if it is a perfect square or a multiple of a square).