Back to matchesWe found a matchYour institution may have access to this item. Find your institution then sign in to continue.TitleAN UPPER BOUND FOR THE NUMBER OF DIOPHANTINE QUINTUPLES.AuthorsBLIZNAC, MARIJA; FILIPIN, ALANAbstractWe 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.SubjectsDIOPHANTINE equations; DIOPHANTINE approximation; APPROXIMATION theory; DIOPHANTINE analysis; LAGRANGE spectrumPublicationBulletin of the Australian Mathematical Society, 2016, Vol 94, Issue 3, p384ISSN0004-9727Publication typeArticleDOI10.1017/S0004972716000423