On the Diophantine equation F(x)=G(y)
Sz. Tengely (2003)
Acta Arithmetica
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Displaying similar documents to “Diophantine undecidability for addition and divisibility in polynomial rings”
On the Diophantine equation F(x)=G(y)
Parametric Solutions of the Diophantine Equation A² + nB⁴ = C³
Susil Kumar Jena (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.
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Franušić, Zrinka (2010)
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Csaba Rakaczki (2003)
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H. G. Grundman, L. L. Hall (2004)
Acta Arithmetica
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Ernst, Bruno (1996)
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H. Kleiman (1976)
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Yang Hai, P. G. Walsh (2010)
Acta Arithmetica
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An irregular D(4)-quadruple cannot be extended to a quintuple
Alan Filipin (2009)
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Parametrizing SL₂(ℤ) and a question of Skolem
Umberto Zannier (2003)
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On simultaneous diophantine equations
Shin-ichi Katayama, Claude Levesque (2003)
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A note on the diophantine equation a²x⁴ - By² = 1
Jianhua Chen (2001)
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A. Berczes, K. Gyory (2002)
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On the Diophantine equation (x² ± C)(y² ± D) = z⁴
Pingzhi Yuan, Jiagui Luo (2010)
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Diophantine equations with Bernoulli polynomials
Manisha Kulkarni, B. Sury (2005)
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Addendum on the equation aX⁴ - bY² = 2
S. Akhtari, A. Togbé, P. G. Walsh (2009)
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Some observations on the Diophantine equation f(x)f(y) = f(z)²
Yong Zhang (2016)
Colloquium Mathematicae
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Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.