Pell’s Equation

In this article we formalize several basic theorems that correspond to Pell’s equation. We focus on two aspects: that the Pell’s equation x² − Dy² = 1 has infinitely many solutions in positive integers for a given D not being a perfect square, and that based on the least fundamental solution of the equation when we can simply calculate algebraically each remaining solution.

“Solutions to Pell’s Equation” are listed as item #39 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.