On quartic Thue equations with trivial solutions

Author:
R. J. Stroeker

Journal:
Math. Comp. **52** (1989), 175-187

MSC:
Primary 11D25

DOI:
https://doi.org/10.1090/S0025-5718-1989-0946605-4

MathSciNet review:
946605

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Abstract: Let **K** be a quartic number field with negative absolute discriminant and let be its real quadratic subfield, with . Moreover, assume **K** to be embedded in the reals. Further, let generate the subgroup of units relative to **L** in the group of positive units of **K**. Under certain conditions, which can be explicitly checked, and for suitable linear forms and with coefficients in , the diophantine equation

*u*and

*v*, has only trivial solutions, that is, solutions given by .

Information on a substantial number of equations of this type and their associated number fields is incorporated in a few tables.

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DOI:
https://doi.org/10.1090/S0025-5718-1989-0946605-4

Article copyright:
© Copyright 1989
American Mathematical Society