@article{article_1554641, title={Diophantine equations on cross-multiplicative forms of the Pell and Pell-Lucas numbers}, journal={Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, volume={27}, pages={464–474}, year={2025}, DOI={10.25092/baunfbed.1554641}, author={Emin, Ahmet and Daşdemir, Ahmet}, keywords={Pell sayısı, Pell-Lucas sayısı, Diophantine denklemler, Matveev teoremi, Dujella-Pethö indirgeme lemması, logaritmaların lineer formları}, 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.}, number={2}, publisher={Balıkesir Üniversitesi}