Diophantine equations with Bernoulli polynomials
Manisha Kulkarni, B. Sury (2005)
Acta Arithmetica
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Manisha Kulkarni, B. Sury (2005)
Acta Arithmetica
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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.
Wolfgang M. Schmidt (2012)
Acta Arithmetica
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Sz. Tengely (2003)
Acta Arithmetica
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Artur Korniłowicz (2017)
Formalized Mathematics
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In this article, we formalize in the Mizar system [3] the notion of the derivative of polynomials over the field of real numbers [4]. To define it, we use the derivative of functions between reals and reals [9].
L. Hajdu, R. Tijdeman (2003)
Acta Arithmetica
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R. Dvornicich, U. Zannier (2011)
Acta Arithmetica
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P. N. Shrivastava (1977)
Publications de l'Institut Mathématique
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Djordjević, Gospava B. (1997)
Matematichki Vesnik
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D. Markovitch (1951)
Matematički Vesnik
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Arun Verma (1975)
Annales Polonici Mathematici
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