Solving The Fermat-Pell’s Equation with Infinite Continuous Fractions
Keywords:
The Fermat-Pell’s equation, infinite continuous fractions, irrational numbersAbstract
The special form is called the Fermat-Pell’s equation where is a positive integer that is not a square. Let's say the solution of this equation is a positive solution as long as x and y are both positive. Since solutions beyond can be arranged in sets of four by sign combinations , it is clear that all solutions will be known once all positive solutions are found. The result which gives us a starting point confirms that any pair of positive integers satisfying the Fermat-Pell’s equation can be obtained from infinite continuous fraction denoting the irrational number √ .References
David M. Burton. (2011). Elementary Number Theory. Tata McGraw-Hill, Sixth Edition.
Gareth A. Jones and J. Mary Jones. (2007). Elementary Number Theory. Springer-Verlag London Limited.
Martin Erickson and Anthony Vazzana. (2010). Introduction to Number Theory. Chapman and Hall/CRC.
Neville Robbins. (2006). Beginning Number Theory. Narosa.
Rosen, Kenneth H. (1984). Elementary number theory and its applications. Addison-Wesley Publishing Company.
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