Prime factors of values of polynomials

• Autorzy: J. Browkin , A. Schinzel
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11N32: Primes represented by polynomials; other multiplicative structure of polynomial values
• 11R11: Quadratic extensions
• 11R27: Units and factorization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 122
• Numer: 1
• Strony: 135-138

Daty

wydano

2011

Twórcy

autor

J. Browkin

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

A. Schinzel

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm122-1-12