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On a Diophantine Equation Concerning the Number of Integer Points in Special Domains

Acta Mathematica Hungarica
Volume/Issue:
Volume 78: Issue 1-2
DOI:
https://doi.org/10.1023/a:1006518403429
Author: L. Hajdu
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On the Diophantine Equations (2 n − 1)(6 n − 1) = x 2 and (a n − 1)(a kn − 1) = x 2

Periodica Mathematica Hungarica
Volume/Issue:
Volume 40: Issue 2
DOI:
https://doi.org/10.1023/a:1010335509489
Authors: Lajos Hajdu and László Szalay
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Cassification of first-order flexible regular bicycle polygons

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 46: Issue 1
DOI:
https://doi.org/10.1556/sscmath.2008.1074
Authors: Robert Connelly and Balázs Csikós

Conway, J. H. and Jones, A. J. , Trigonometric diophantine equations (On vanishing sums of roots of unity), Acta Arith. , 30 (1976), 229–240. MR 54#10141 Jones A. J

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On a family of cubics over imaginary quadratic fields

Periodica Mathematica Hungarica
Volume/Issue:
Volume 51: Issue 2
DOI:
https://doi.org/10.1007/s10998-005-0032-6
Author: Volker Ziegler

Summary  

We consider the relative Thue equations \[X^3 - t X^2 Y - (t+1) X Y^2 -Y^3=\mu,\] where the parameter \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $t$ \end{document}, the root of unity \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mu$ \end{document} and the solutions \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $X$ \end{document} and \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $Y$ \end{document} are integers in the same imaginary quadratic number field. We use Baker's method to find all solutions for \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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $|t|> 2.88 \cdot 10^{33}$ \end{document}.

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Polynomial-exponential equations involving multi-recurrences

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 46: Issue 3
DOI:
https://doi.org/10.1556/sscmath.2009.1098
Author: Clemens Fuchs

exponential Diophantine equations. I. Fibonacci and Lucas perfect powers, Ann. of Math. (2) 163 (2006), no. 3, 969–1018. MR 2007f :11031 Siksek S. Classical and modular approaches

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On the diophantine equation \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} \(\left( {\left( {_n^x } \right)} \right) = b\left( {_m^y } \right)\) \end{document}

Periodica Mathematica Hungarica
Volume/Issue:
Volume 49: Issue 2
DOI:
https://doi.org/10.1007/s10998-004-0527-6
Author: Cs. Rakaczki
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ON A COMBINATORIAL PAPER O KISS AND ZAY

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 37: Issue 1-2
DOI:
https://doi.org/10.1556/sscmath.37.2001.1-2.12
Author: P. Bundschuh

SHOREY, T. N. and TIJDEMAN, R., Exponential Diophantine equations Cambridge Tracts in Mathematics, 87, Cambridge University Press, Cambridge - New York, 1986. MR 88h :11002

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Stanley’s conjecture for critical ideals

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 48: Issue 2
DOI:
https://doi.org/10.1556/sscmath.2010.1160
Authors: Azeem Haider and Sardar Khan

. 2010 38 773 784 Stanley, R. P. , Linear Diophantine equations and local cohomology, Invent. Math. , 68

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On biquadratic fields that admit unit power integral basis

Acta Mathematica Hungarica
Volume/Issue:
Volume 133: Issue 3
DOI:
https://doi.org/10.1007/s10474-011-0103-5
Authors: Attila Pethő and Volker Ziegler

] Chen , J. H. , Voutier , P. 1997 Complete solution of the Diophantine equation X 2 +1= dY 4 and a related family of quartic Thue equations J. Number Theory 62 71 – 99 10.1006/jnth.1997.2018 . [7

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Stanley depth of edge ideals

Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 49: Issue 4
DOI:
https://doi.org/10.1556/sscmath.49.2012.4.1223
Authors: Muhammad Ishaq and Muhammad Qureshi

Stanley, R. , Linear Diophantine equations and local cohomology, Invent. Math. , 68 (1982), 175–193. Stanley R. Linear Diophantine equations and local cohomology

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