Premium
Thue and Thue–Mahler Equations over Rings of Integers
Author(s) -
Smart N. P.
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610797005619
Subject(s) - thue equation , mathematics , algebraic number field , exponential function , unit (ring theory) , ring of integers , field (mathematics) , ring (chemistry) , discrete mathematics , diophantine equation , pure mathematics , mathematical analysis , diophantine set , mathematics education , chemistry , organic chemistry
A method is given to solve any Thue–Mahler equation when the coefficients and variables come from the ring of integers of a number field. The method involves using an algorithm for solving an S ‐unit equation and a method of reducing the number of exponential variables. The method is used to solve the equationX 3 ‐ Y 32 = ± 5 n f o r X , Y ∈ Z [ 2 ] .