Pell ve Pell-Lucas sayılarının karşılıklı çarpımsal eşitlikleri ile ilgili Diophantine denklemleri

Öz

Bu çalışma, logaritmalardaki lineer formlara dayalı olarak geliştirilen Matveev’s teoremi ve Dujella-Pethő indirgeme lemması kullanılarak, iki rastgele Pell-Lucas sayısının çarpımı olan tüm Pell sayıları ve iki rastgele Pell sayısının çarpımı olan tüm Pell-Lucas sayılarını araştırmayı amaçlamaktadır. Ayrıca, Pell ve Pell-Lucas sayılarına ait ortak terimler incelenmiş ve hiçbir Pell sayısının bir Pell-Lucas sayısının karesi olamayacağı gibi, hiçbir Pell-Lucas sayısının da bir Pell sayısının karesi olarak yazılamayacağı gösterilmiştir.

Anahtar Kelimeler

• Pell sayısı
• Pell-Lucas sayısı
• Diophantine denklemler
• Matveev teoremi
• Dujella-Pethö indirgeme lemması
• logaritmaların lineer formları

Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbers

Öz

This study aims to explore all Pell numbers that are the product of two random Pell-Lucas numbers and all Pell-Lucas numbers that are the product of two random Pell numbers based on linear forms in logarithms of algebraic numbers using Matveev's theorem and Dujella - Pethő reduction lemma. Further, we find all the common terms of Pell and Pell-Lucas numbers and show that no Pell and no Pell-Lucas numbers can be written as a square of another.

Anahtar Kelimeler

• Pell number
• Pell-Lucas number
• Diophantine equation
• Matveev's theorem
• Dujella-Pethö reduction lemma
• linear forms in logarithms

Kaynakça

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