Thue and Thue–Mahler Equations over Rings of Integers | Zendy

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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 ] .

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