Pell's equation

Pell's equation is a mathematical relationship expressed as x² - D*y² = 1, where D is a positive non-square integer, and x and y are integers to be found. It's a type of Diophantine equation, seeking exact whole number solutions. The equation arises in number theory and has connections to quadratic forms and units in algebraic number fields. Solutions are infinite, generated through specific algorithms, and help understand fundamental properties of numbers, especially in quadratic integers. Overall, Pell's equation explores the deep relationships between squares, products, and number structure.