On polynomials taking small values at integral arguments II
Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)
Acta Arithmetica
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Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)
Acta Arithmetica
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H. Kaufman, Mira Bhargava (1965)
Collectanea Mathematica
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Štefan Schwarz (1988)
Mathematica Slovaca
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Christoph Schwarzweller (2017)
Formalized Mathematics
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In this article we further extend the algebraic theory of polynomial rings in Mizar [1, 2, 3]. We deal with roots and multiple roots of polynomials and show that both the real numbers and finite domains are not algebraically closed [5, 7]. We also prove the identity theorem for polynomials and that the number of multiple roots is bounded by the polynomial’s degree [4, 6].
Caragiu, Mihai (2001)
International Journal of Mathematics and Mathematical Sciences
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M. Filaseta, T.-Y. Lam (2002)
Acta Arithmetica
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Matthews, R., Lidl, R. (1988)
International Journal of Mathematics and Mathematical Sciences
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Andrej Dujella, Tomislav Pejković (2011)
Rendiconti del Seminario Matematico della Università di Padova
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Yu-Ru Liu (2004)
Acta Arithmetica
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Meyn, Helmut, Götz, Werner (1989)
Séminaire Lotharingien de Combinatoire [electronic only]
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Ewa Ligocka (2007)
Annales Polonici Mathematici
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We extend the results obtained in our previous paper, concerning quasiregular polynomials of algebraic degree two, to the case of polynomial endomorphisms of ℝ² whose algebraic degree is equal to their topological degree. We also deal with some other classes of polynomial endomorphisms extendable to ℂℙ².
C. Fong, G. Lumer, E. Nordgren, H. Radjavi, P. Rosenthal (1995)
Studia Mathematica
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We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.
Mira Bhargava (1964)
Collectanea Mathematica
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Shih Ping Tung (2006)
Acta Arithmetica
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