Formalization of Pell's equation in the mizar system

摘要

We present a case study on a formalization of a textbook theorem that is listed as #39 at Freek Wiedijk's list of “Top 100 mathematical theorems”. We focus on the formalization of the theorem that Pell's equation x2 - Dy2 = 1 has infinitely many solutions in positive integers for a given non square natural number D. We present also a formalization of the theorem that based on the least fundamental solution of the equation we can simply calculate algebraically each remaining solution.