Pell's equation is a type of mathematical equation that takes the form x^2 - Dy^2 = 1, where D is a non-square positive integer, and x and y are integers. This equation is named after the mathematician John Pell, although he did not actually discover it. The solutions to Pell's equation are important in number theory and have applications in various areas of mathematics. Finding solutions to Pell's equation involves determining pairs of integers (x, y) that satisfy the equation. The solutions can be generated using continued fractions, particularly for the square root of D. Pell's equation has a rich history and has been studied for centuries, leading to many interesting mathematical discoveries.