APPLICATION TO PELL’S EQUATIONS
Keywords:
Pell’s equation, perfect square, Hilbert’s 10th problem, fundamental solution, matrix of the Pell’s equation, multiplication principle, sequence, recursive system, eigenvalues, characteristic equation, Pell resolvent equation, prime numbers, positive integer numbers.Abstract
This article reflects on the Pell’s equations, one of the Diophantine equations (i.e. equations requiring a solution in integers). All solutions to this equation have been found and an overview is given. The general solution to the Pell’s equation using matrices is an easy-to-define method. The application of the Pell’s equations has been described. Solutions to complex Olympic problems are given. At the end of the article, enough problems are given to work independently.
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