Almost-primes represented by quadratic polynomials
Robert J. Lemke Oliver (2012)
Acta Arithmetica
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Robert J. Lemke Oliver (2012)
Acta Arithmetica
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Kaisa Matomäki (2009)
Acta Arithmetica
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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.
Gihan Marasingha (2006)
Acta Arithmetica
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Křížek, Michal, Luca, Florian, Shparlinski, Igor E., Somer, Lawrence (2011)
Journal of Integer Sequences [electronic only]
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Mollin, Richard A. (1990)
International Journal of Mathematics and Mathematical Sciences
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W. Narkiewicz (1981)
Colloquium Mathematicae
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Lilu Zhao (2014)
Acta Arithmetica
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By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.
W. Narkiewicz (1966)
Acta Arithmetica
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Vladimir Janković (2005)
The Teaching of Mathematics
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Strebel, Kurt (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Halter-Koch, Franz (1985)
Manuscripta mathematica
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Mohamed Ayad, Donald L. McQuillan (2001)
Acta Arithmetica
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Heima Hayashi (2011)
Acta Arithmetica
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