Pell's equation is a mathematical equation of the form x2 - Dy2 = 1, where D is a non-square positive integer. It is named after the mathematician John Pell who studied it in the 17th century.
A Diophantine equation is a polynomial equation with integer coefficients, where the solutions are required to be integers as well. It is named after the Greek mathematician Diophantus who studied these types of equations.
Pell's equation is a special case of the more general Diophantine equation. It can be transformed into a Diophantine equation by setting D = 1. Therefore, the techniques used to solve Diophantine equations can also be applied to Pell's equation.
These equations have applications in number theory, cryptography, and geometry. They can also be used to solve problems in physics, such as finding integer solutions to equations in quantum mechanics.
Yes, there are many resources available online and in books for learning about these equations. Some recommended resources include "An Introduction to Diophantine Equations" by Titu Andreescu and Dorin Andrica, and "Pell's Equation" by Edward J. Barbeau.