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On Diophantine quintuples and D(-1)-quadruples (CROSBI ID 195337)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Elsholtz, Christian ; Filipin, Alan ; Fujita, Yasutsugu
On Diophantine quintuples and D(-1)-quadruples // Monatshefte für Mathematik, 175 (2014), 2; 227-239. doi: 10.1007/s00605-013-0571-5
Podaci o odgovornosti
Elsholtz, Christian ; Filipin, Alan ; Fujita, Yasutsugu
engleski
On Diophantine quintuples and D(-1)-quadruples
In this paper the known upper bound 10^96 for the number of Diophantine quintuples is reduced to 5.32*10^32. The key ingredient for the improvement is that certain individual bounds on parameters are now combined with a more efficient counting of tuples, and estimated by sums over divisor functions. As a side effect, we also improve the known upper bound 4*10^70 for the number of D(-1)-quadruples to 5*10^60.
Diophantine tuples; system of Diophantine equations
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