An absolute bound for the size of Diophantine \(m\)-tuples
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Publication:1597955
DOI10.1006/jnth.2000.2627zbMath1010.11019OpenAlexW2087416278MaRDI QIDQ1597955
Publication date: 4 June 2002
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jnth.2000.2627
Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)
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Cites Work
- Simultaneous Pell equations
- Explicit bounds for the solutions of elliptic equations with rational coefficients
- On the resolution of index form equations in biquadratic number fields. III: The bicyclic biquadratic case
- Logarithmic forms and group varieties.
- A proof of the Hoggatt-Bergum conjecture
- Solving constrained Pell equations
- The Diophantine Equation y 2 = ax 3 +bx 2 +cx +d
- THE EQUATIONS 3x2−2 = y2 AND 8x2−7 = z2
- On the number of solutions of simultaneous Pell equations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
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