İkinci dereceden genel diophantine denklemlerinin özel çözümleri üzerine
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Date
2014-12-26
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Selçuk Üniversitesi Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Bu çalışmada uzun bir geçmişe sahip olan Diophantine denklemleri incelenmiştir ve özel olarak da ikinci dereceden Diophantine denklemlerinin tamsayı çözümleri araştırılmıştır. Bu yapılırken denklemlere çeşitli dönüşümler uygulanmış ve Pell tipindeki denklemlere indirgenmiştir. Bu denklemlerin genel çözümleri sürekli kesir açılımları kullanılarak formüle edilmiştir. Buna ilaveten bazı Diophantine denklemlerinin genelleştirilmiş Fibonacci ve Lucas sayı çözümleri bulunmuştur.
In this study, Diophantine equations which have a long history are examined and specially, integer solutions of quadratic Diophantine equations were searched. While doing this, various transformations were applied to the equations to reduce them to the Pellian type equations. Using continued fraction expansions of this equations, general solutions were formulated. In addition to these, generalized Fibonacci and Lucas number solutions of some Diophantine equations were obtained.
In this study, Diophantine equations which have a long history are examined and specially, integer solutions of quadratic Diophantine equations were searched. While doing this, various transformations were applied to the equations to reduce them to the Pellian type equations. Using continued fraction expansions of this equations, general solutions were formulated. In addition to these, generalized Fibonacci and Lucas number solutions of some Diophantine equations were obtained.
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Diofant denklemleri, Diophantine equations, Fibonacci sayıları, Fibonacci numbers, Lucas sayıları, Lucas numbers, Pell denklemi, Pell equation, Tam sayı çözümleri, Integer solutions
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Citation
Peker, B. (2014). İkinci dereceden genel diophantine denklemlerinin özel çözümleri üzerine. Selçuk Üniversitesi, Yayımlanmış doktora tezi, Konya.
