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  • 1 University of Zagreb Department of Mathematics Bijenička cesta 30 10000 Zagreb Croatia
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We characterize the existence of infinitely many Diophantine quadruples with the property D ( z ) in the ring ℤ[1 +
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sqrt d$$ \end{document}
)/2], where d is a positive integer such that the Pellian equation x2dy2 = 4 is solvable, in terms of representability of z as a difference of two squares.
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