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Journals / Adıyaman Üniversitesi Fen Bilimleri Dergisi / 2025 / Cilt: 15 Sayı: 2

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

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

Ahmet Daşdemir(KASTAMONU ÜNİVERSİTESİ)0000-0001-8352-2020
Ahmet Emin(KARABÜK ÜNİVERSİTESİ)0000-0001-7791-7181
Pages
217–227
Publication Date
2025-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our proof is conducted with the famous Matveev theorem and Dujella-Pethő reduction lemma.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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 .
📊
Key Findings & Data: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 .
💡
Conclusion & Impact:Our proof is conducted with the famous Matveev theorem and Dujella-Pethő reduction lemma.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Pell sayısı · Modifiye Pell-Lucas sayısı · Diophantine denklemi

Abstract

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.

Özet

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.

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Cite This Article

Daşdemir, A., Emin, A. (2025). On the Solutions of the Diophantine Equations P_k=R_m R_n and R_k=P_m P_n. Adıyaman Üniversitesi Fen Bilimleri Dergisi, Cilt: 15 Sayı: 2, 217–227. https://doi.org/10.37094/adyujsci.1666370

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