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

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Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Cilt: 27 Sayı: 2
Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbers

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

Authors : Ahmet Emin, Ahmet Daşdemir

Pages : 464-474

Doi:10.25092/baunfbed.1554641

View : 104 | Download : 172

Publication Date : 2025-07-15

Article Type : Research Paper

Abstract :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.
Keywords : Pell sayısı, Pell-Lucas sayısı, Diophantine denklemler, Matveev teoremi, Dujella-Pethö indirgeme lemması, logaritmaların lineer formları

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