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Solution of Pell Equations

Narinder Kumar Wadhawan , Priyanka Wadhawan

Abstract



In this paper, Pell equations have been solved by untraditional methods whereby besides other approaches, factorisation of n as well as n.y^ squared has been resorted to by assigning different integer values to y where x,n and p are all integers and n is not a whole square. Once n or n.y^ squared as the case may be, is factorised, fundamental values of x and y are obtained by simple formulae derived in this paper. Using properties of surds and Binomial expansion, family of solutions of Pell equations are obtained. An algorithm for solving Pell equations has also been found and given in the paper. Methods used are simple, untraditional and easy to understand by students and scholars alike.


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