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

nije evidentirano