Arithmetic properties of polynomial specializations over finite fields
Paul Pollack (2009)
Acta Arithmetica
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Paul Pollack (2009)
Acta Arithmetica
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Dress, François, Olivier, Michel (1999)
Experimental Mathematics
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Michael Filaseta (1988)
Acta Arithmetica
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Hongze Li, Hao Pan (2009)
Acta Arithmetica
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Michael Filaseta, Manton Matthews, Jr. (2004)
Colloquium Mathematicae
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If f(x) and g(x) are relatively prime polynomials in ℤ[x] satisfying certain conditions arising from a theorem of Capelli and if n is an integer > N for some sufficiently large N, then the non-reciprocal part of f(x)xⁿ + g(x) is either identically ±1 or is irreducible over the rationals. This result follows from work of Schinzel in 1965. We show here that under the conditions that f(x) and g(x) are relatively prime 0,1-polynomials (so each coefficient is either 0 or 1) and f(0) =...
J. Browkin, A. Schinzel (2011)
Colloquium Mathematicae
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We prove that for every quadratic binomial f(x) = rx² + s ∈ ℤ[x] there are pairs ⟨a,b⟩ ∈ ℕ² such that a ≠ b, f(a) and f(b) have the same prime factors and min{a,b} is arbitrarily large. We prove the same result for every monic quadratic trinomial over ℤ.
L. Hajdu, R. Tijdeman (2003)
Acta Arithmetica
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K. Ramachandra (1971)
Acta Arithmetica
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D. Markovitch (1951)
Matematički Vesnik
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Magdalena Jastrzebska, Adam Grabowski (2006)
Formalized Mathematics
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We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is...
Jiahai Kan (2004)
Acta Arithmetica
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Milnes, Paul, Stanley-Albarda, C. (1997)
International Journal of Mathematics and Mathematical Sciences
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J. Turk (1980)
Journal für die reine und angewandte Mathematik
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D. K. Basu (1975)
Matematički Vesnik
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