Complete solutions to families of quartic Thue equations
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- by Attila Pethő PDF
- Math. Comp. 57 (1991), 777-798 Request permission
Abstract:
Using a method due to E. Thomas, we prove that if $|a| > 9.9 \cdot {10^{27}}$ then the Diophantine equations \[ {x^4} - a{x^3}y - {x^2}{y^2} + ax{y^3} + {y^4} = 1\] and \[ {x^4} - a{x^3}y - 3{x^2}{y^2} + ax{y^3} + {y^4} = \pm 1\] have exactly twelve solutions, namely $(x,y) = (0, \pm 1), ( \pm 1,0), ( \pm 1, \pm 1), ( \mp 1, \pm 1), ( \pm a, \pm 1), ( \pm 1, \mp a)$ and eight solutions, $(x,y) = (0, \pm 1), ( \pm 1,0), ( \pm 1, \pm 1), ( \pm 1, \mp 1)$ , respectively.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 57 (1991), 777-798
- MSC: Primary 11D25
- DOI: https://doi.org/10.1090/S0025-5718-1991-1094956-7
- MathSciNet review: 1094956