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

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

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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