JP Journal of Algebra, Number Theory and Applications
Volume 42, Issue 1, Pages 15 - 32
(April 2019) http://dx.doi.org/10.17654/NT042010015 |
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PELL’S EQUATIONS IN GAUSSIAN INTEGERS
Algracia Kharbuki and Madan Mohan Singh
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Abstract: From Hurwitz’s approach of complex continued fractions, we build a complex theory of the Pell’s equation. In this paper, we study the complex theory of the Pell’s equation, that is, finding its solutions in Gaussian integers, using Hurwitz complex continued fraction, hence, generalizing it to the Pell’s equation and in the process we also develop some interesting properties. |
Keywords and phrases: complex continued fraction, Hurwitz continued fraction, recurrence relation, Pell’s equation, Gaussian integers.
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