Solving Simultaneous Modular Equations of Low Degree
✍ Scribed by Hastad, Johan
- Book ID
- 118174152
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1988
- Tongue
- English
- Weight
- 684 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0097-5397
- DOI
- 10.1137/0217019
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📜 SIMILAR VOLUMES
We propose a general method for numerical solution of Thue equations, which allows one to solve in reasonable time Thue equations of high degree (provided necessary algebraic number theory data is available). We illustrate our method, solving completely concrete Thue equations of degrees 19 and 33.
If a and b are distinct positive integers then a previous result of the author implies that the simultaneous Diophantine equations x 2 &az 2 =y 2 &bz 2 =1 possess at most 3 solutions in positive integers (x, y, z). On the other hand, there are infinite families of distinct integers (a, b) for which