Linear combinations of prime powers in binary recurrence sequences

DOI10.1142/S1793042117500166zbMath1409.11009MaRDI QIDQ2965766

Zsolt Rábai, Csanád Bertók, István Pink, Lajos Hajdu

Publication date: 3 March 2017

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

recurrence sequenceslocal methodssums of prime powersexponential congruences

Mathematics Subject Classification ID

Recurrences (11B37) Diophantine equations in many variables (11D72)

Related Items (12)

Sums of \(S\)-units in recurrence sequences ⋮ \(k\)-Fibonacci powers as sums of powers of some fixed primes ⋮ Sums of \(S\)-units in sum of terms of recurrence sequences ⋮ Sums of \(S\)-units in the solution sets of generalized Pell equations ⋮ Effective resolution of Diophantine equations of the form \(u_n+u_m=w p_1^{z_1} \dotsm p_s^{z_s}\) ⋮ Linear combinations of prime powers in sums of terms of binary recurrence sequences ⋮ Linear combinations of prime powers in \(X\)-coordinates of Pell equations ⋮ A Hasse-type principle for exponential Diophantine equations over number fields and its applications ⋮ On the exponential Diophantine equation P^x _n + P ^x _n+1 + ⋯ + P ^x _n+k-1 = P_m ⋮ Nonnegative integer solutions of the equationFn ⋮ On the exponential Diophantine equation Pxn+Pxn+1=Pm ⋮ Prime powers in sums of terms of binary recurrence sequences

Uses Software

• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fibonacci and Lucas numbers of the form \(2^a+3^b+5^c\)
• Combinatorial numbers in binary recurrences
• Perfect powers in second order linear recurrences
• The Magma algebra system. I: The user language
• Linear combinations of factorials and \(S\)-units in a binary recurrence sequence
• 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
• A Hasse-type principle for exponential Diophantine equations and its applications
• Carmichael's lambda function
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.

This page was built for publication: Linear combinations of prime powers in binary recurrence sequences