On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
Stroeker, Roel J., de Weger, Benjamin M.M. (1994)
Experimental Mathematics
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Displaying similar documents to “Diophantine equations of matching games II”
On elliptic diophantine equations that defy Thue's method: The case of the Ochoa curve.
Solving elliptic diophantine equations avoiding Thue equations and elliptic logarithms.
de Weger, Benjamin M.M. (1998)
Experimental Mathematics
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The D(1)-extensions of D(-1)-triples 1,2,c and integer points on the attached elliptic curves
Yasutsugu Fujita (2007)
Acta Arithmetica
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On the equation aX⁴-bY² = 2
S. Akhtari, A. Togbé, P. G. Walsh (2008)
Acta Arithmetica
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On a few Diophantine equations, in particular, Fermat's Last Theorem.
Levesque, C. (2003)
International Journal of Mathematics and Mathematical Sciences
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On the diophantine equation f(x)f(y) = f(z)²
Maciej Ulas (2007)
Colloquium Mathematicae
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Let f ∈ ℚ [X] and deg f ≤ 3. We prove that if deg f = 2, then the diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in ℚ (t). In the case when deg f = 3 and f(X) = X(X²+aX+b) we show that for all but finitely many a,b ∈ ℤ satisfying ab ≠ 0 and additionally, if p|a, then p²∤b, the equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in rationals.
On the diophantine equation f (x, y) = 0.
H. Kleiman (1976)
Journal für die reine und angewandte Mathematik
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On a Diophantine problem of Bennett
Yang Hai, P. G. Walsh (2010)
Acta Arithmetica
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On simultaneous diophantine equations
Shin-ichi Katayama, Claude Levesque (2003)
Acta Arithmetica
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An irregular D(4)-quadruple cannot be extended to a quintuple
Alan Filipin (2009)
Acta Arithmetica
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On a Diophantine equation involving factorials.
Ernst, Bruno (1996)
General Mathematics
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A note on the diophantine equation a²x⁴ - By² = 1
Jianhua Chen (2001)
Acta Arithmetica
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The Diophantine equation xⁿ = Dy² + 1
J. H. E. Cohn (2003)
Acta Arithmetica
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Addendum on the equation aX⁴ - bY² = 2
S. Akhtari, A. Togbé, P. G. Walsh (2009)
Acta Arithmetica
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Recipes for Solving Diophantine Problems by Baker's Method
W. J. Ellison (1970-1971)
Séminaire de théorie des nombres de Bordeaux
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On the Diophantine equation (x² ± C)(y² ± D) = z⁴
Pingzhi Yuan, Jiagui Luo (2010)
Acta Arithmetica
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Division-ample sets and the Diophantine problem for rings of integers
Gunther Cornelissen, Thanases Pheidas, Karim Zahidi (2005)
Journal de Théorie des Nombres de Bordeaux
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We prove that Hilbert’s Tenth Problem for a ring of integers in a number field has a negative answer if satisfies two arithmetical conditions (existence of a so-called set of integers and of an elliptic curve of rank one over ). We relate division-ample sets to arithmetic of abelian varieties.