On the Solutions of the Diophantine Equations P_k=R_m R_n and R_k=P_m P_n

Yıl 2025, Cilt: 15 Sayı: 2, 217 - 227, 31.12.2025

Ahmet Daşdemir , Ahmet Emin

https://doi.org/10.37094/adyujsci.1666370

https://izlik.org/JA27UM95NK

Öz

This study aims to find all possible solutions (k,m,n) of the Diophantine equations P_k=R_m R_n and R_k=P_m P_n . Our proof is conducted with the famous Matveev theorem and Dujella-Pethő reduction lemma.

Anahtar Kelimeler

Pell number , Modified Pell-Lucas number , Diophantine equation , Matveev theorem , Linear forms in logarithms , Dujella-Pethő lemma

P_k=R_m R_n ve R_k=P_m P_n Diophantine Denklemlerinin Çözümleri Üzerine

https://izlik.org/JA27UM95NK

Öz

Bu çalışma, P_k=R_m R_n ve R_k=P_m P_n Diophantine denklemleri için tüm olası çözümleri olan (k,m,n) üçlülerini belirlemeyi amaçlamaktadır. Bu çözümleri araştırmak için ortaya koyduğumuz teoremin ispatında, Matveev teoremi ve Dujella-Pethő indirgeme lemmasından yararlanılmıştır.

Anahtar Kelimeler

Pell sayısı , Modifiye Pell-Lucas sayısı , Diophantine denklemi , Matveev teoremi , Logaritmaların lineer formları , Dujella-Pethö lemması

Kaynakça

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