Bazı Pell Denklemlerinin Temel Çözümleri

Yıl 2013, Cilt: 17 Sayı: 1, 125 - 129, 01.04.2013

Merve Güney Refik Keskin

Öz

Let a,b and n are positive integers. In this paper, we find continued fraction expansion of √d when d=a^2 b^2+2b, a^2 b^2+b,a^2±2,a^2±a. We will use continued fraction expansion of √d in order to get the fundamental solutions to the equations x²-dy²=±1 when d=a^2 b^2+2b, a^2 b^2+b,a^2±2,a^2±a

Anahtar Kelimeler

Diophant Denklemleri, Pell Denklemleri, Sürekli Kesirler.

Fundamental Solutions to Some Pell Equations

Öz

Let

Anahtar Kelimeler

Diophantine Equations, Pell Equations, Continued Fractions.

Kaynakça

• Adler, A. and Coury, J. E., The Theory of Numbers: A Text and Source Book of Problems, Jones and Bartlett Publishers, Boston, MA, 1995.
• R. Mollin, Fundamental Number Theory with Applications, Crc Press, 1998.
• T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1981.
• Don Redmond, Number Theory: An Introduction, Markel Dekker, Inc, 1996.
• John P. Robertson, Solving the generalized Pell equation