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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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Al-Rashed A. , 'Some Diophantine quadruples in the ring ℤ[ % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqipC0xg9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaarm % qr1ngBPrgitLxBI9gBaGqbaiab-jHiTiab-jdaYaWcbeaaaaa!3C78! \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} $$\sqrt { - 2}$$ \end{document}] ' (2004 ) 9 Math. Commun. : 1 -8.

• Baker, A. and Davenport, H. , The equations 3 x2 − 2 = y2 and 8 x2 − 7 = z2 , Quart. J. Math. Oxford Ser. (2) , 20 (1969), 129–137. MR40 #1333

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Dujella A. , 'Some polynomial formulas for Diophantine quadruples ' (1996 ) 328 Grazer Math. Ber. : 25 -30.

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Dujella A. , 'The problem of Diophantus and Davenport for Gaussian integers ' (1997 ) 32 Glas. Mat. Ser. III : 1 -10.

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Franušić Z. , 'On differences of two squares in some quadratic fields ' (2007 ) 37 Rocky Mountain J. Math. : 429 -453.

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• Franušić, Z. , Diophantine quadruples in the ring ℤ[\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} $$\sqrt 2$$ \end{document}], Math. Commun. , 9 (2004), 141–148. MR2005k :11057

Franušić Z. , '' (2004 ) 9 Diophantine quadruples in the ring ℤ[√2], Math. Commun. : 141 -148.

• Franušić, Z. , Diophantine quadruples in ℤ[\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} $$\sqrt {4k + 3}$$ \end{document}], preprint.

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 2020 Total Cites 536 WoS Journal Impact Factor 0,855 Rank by Mathematics 189/330 (Q3) Impact Factor Impact Factor 0,826 without Journal Self Cites 5 Year 1,703 Impact Factor Journal 0,68 Citation Indicator Rank by Journal Mathematics 230/470 (Q2) Citation Indicator Citable 32 Items Total 32 Articles Total 0 Reviews Scimago 24 H-index Scimago 0,307 Journal Rank Scimago Mathematics (miscellaneous) Q3 Quartile Score Scopus 139/130=1,1 Scite Score Scopus General Mathematics 204/378 (Q3) Scite Score Rank Scopus 1,069 SNIP Days from 85 sumbission to acceptance Days from 123 acceptance to publication Acceptance 16% Rate

2019
Total Cites
WoS
463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites
0,468
5 Year
Impact Factor
0,413
Immediacy
Index
0,135
Citable
Items
37
Total
Articles
37
Total
Reviews
0
Cited
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Citing
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Eigenfactor
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0,00039
Article Influence
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0,196
% Articles
in
Citable Items
100,00
Normalized
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0,04841
Average
IF
Percentile
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Scimago
H-index
23
Scimago
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Scopus
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76/104=0,7
Scopus
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Studia Scientiarum Mathematicarum Hungarica
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2021 Volume 58
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