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An upper bound for the number of diophantine quintuples. (English) Zbl 1419.11052

Summary: We improve the known upper bound for the number of Diophantine \(D(4)\)-quintuples by using the most recent methods that were developed in the \(D(1)\) case. More precisely, we prove that there are at most \(6.8587\times 10^{29}\) \(D(4)\)-quintuples.

MSC:

11D09 Quadratic and bilinear Diophantine equations
11D45 Counting solutions of Diophantine equations
11J86 Linear forms in logarithms; Baker’s method
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