On the Diophantine equation \(P_m=P_n^x+P_{n+1}^x\) with Padovan numbers

DOI10.1007/s40590-022-00420-zzbMath1498.11102OpenAlexW4214944155MaRDI QIDQ2116817

Santos Hernández Hernández, Ana Cecilia García Lomelí

Publication date: 18 March 2022

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-022-00420-z

zbMATH Keywords

continued fractionslinear forms in logarithmsreduction methodPadovan sequence

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Uses Software

• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linear combinations of factorials and \(S\)-units in a binary recurrence sequence
• An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers
• An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers
• On the exponential Diophantine equation Pxn+Pxn+1=Pm
• Powers of two as sums of two k-Fibonacci numbers
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²