A polynomial variant of a problem of Diophantus and Euler

DOI10.1216/rmjm/1181069929zbMath1074.11019OpenAlexW1969141707MaRDI QIDQ1430421

Andrej Dujella, Clemens Fuchs

Publication date: 27 May 2004

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069929

zbMATH Keywords

polynomial diophantine equationsbinary linear recurrenceproblem of Diophantos

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Recurrences (11B37) Polynomials in number theory (11C08)

Related Items (10)

Divisibility by 2 on quartic models of elliptic curves and rational Diophantine \(D(q)\)-quintuples ⋮ A POLYNOMIAL VARIANT OF A PROBLEM OF DIOPHANTUS FOR PURE POWERS ⋮ Complete solution of the polynomial version of a problem of Diophantus ⋮ Diophantine \(m\)-tuples for linear polynomials. II: Equal degrees ⋮ On a problem of Diophantus with polynomials ⋮ On the size of sets in which \(xy + 4\) is always a square ⋮ ON THE SIZE OF SETS IN A POLYNOMIAL VARIANT OF A PROBLEM OF DIOPHANTUS ⋮ Diophantine quadruples in \(\mathbb{Z}[i[X]\)] ⋮ Unnamed Item ⋮ On the existence of \(D(-3)\)-quadruples over \(\mathbb{Z}\)

Cites Work

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• The simultaneous diophantine equations \(5Y^ 2-20=X^ 2\) and \(2Y^ 2+1=Z^ 2\)
• An absolute bound for the size of Diophantine \(m\)-tuples
• On the size of Diophantine m-tuples
• Sets in Which xy + k is Always a Square
• A VARIATION ON A PROBLEM OF DAVENPORT AND DIOPHANTUS
• Solving constrained Pell equations
• There are only finitely many Diophantine quintuples
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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