Professional paper

Some reviews on the Pell equation

Željko Zrno ; Veleučilište Marko Marulić u Kninu, Knin. Hrvatska

Abstract

In this paper we will discuss a class of Diophant equations known in the literature as the Pellian equation, $x^2-dy^2=1, x,y \in \mathbb{N}$, \\ \mbox{$d \in \mathbb{N}\setminus \{1,4,9,...,n^2,...\}$}. We will give several approaches to solving the equation: the fundamental solution of the equation and relations to infinitely many other solutions, the geometric interpretation of the Pellian equation, and the recursive relations for the solutions of the Pellian equation.

Keywords

equation; fundamental solutions; unimodular transformation; recursion

Hrčak ID:

100524

URI

https://hrcak.srce.hr/100524

Publication date:

23.4.2013.

Article data in other languages: croatian

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