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In this article we have used new methods to improve the known upper bound on the number of D(4)-quintuples. As in D(1) case, it is conjectured that no D(4)-quintuple exist, and moreover, that every quadruple is regular.

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This page is a summary of: AN UPPER BOUND FOR THE NUMBER OF DIOPHANTINE QUINTUPLES, Bulletin of the Australian Mathematical Society, August 2016, Cambridge University Press,
DOI: 10.1017/s0004972716000423.
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