A Hasse-type principle for exponential Diophantine equations over number fields and its applications

DOI10.1007/s00605-018-1169-8zbMath1437.11050OpenAlexW2794248482WikidataQ115606434 ScholiaQ115606434MaRDI QIDQ1795159

Lajos Hajdu, Csanád Bertók

Publication date: 16 October 2018

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-018-1169-8

zbMATH Keywords

exponential Diophantine equationsSkolem's conjecture

Mathematics Subject Classification ID

Congruences in many variables (11D79) Exponential Diophantine equations (11D61)

Related Items (3)

Skolem's conjecture confirmed for a family of exponential equations. III. ⋮ The resolution of three exponential Diophantine equations in several variables ⋮ Skolem’s conjecture confirmed for a family of exponential equations, II

Uses Software

• Magma

Cites Work

• Small points on subvarieties of a torus
• Generalized balancing numbers
• Fermat-Euler theorem in algebraic number fields
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• The Magma algebra system. I: The user language
• Linear equations in variables which lie in a multiplicative group
• On a problem of Pillai with Fibonacci numbers and powers of 2
• A Hasse-type principle for exponential Diophantine equations and its applications
• Balancing numbers which are products of consecutive integers
• Representing integers as linear combinations of powers
• Unit Equations in Diophantine Number Theory
• Linear combinations of prime powers in binary recurrence sequences
• A simple proof of a theorem of Hajdu–Jarden–Narkiewicz
• Representing integers as linear combinations of S-units
• Carmichael's lambda function
• Addendum and corrigendum to the paper "Abelian binomials, power residues and exponential congruences", Acta Arith. 32(1977), pp. 245-274
• On power residues
• Abelian binomials, power residues and exponential congruences
• On the exponential local-global principle
• On a variant of Pillai’s problem
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