Prime factors of values of polynomials
Colloquium Mathematicae (2011)
- Volume: 122, Issue: 1, page 135-138
- ISSN: 0010-1354
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topJ. Browkin, and A. Schinzel. "Prime factors of values of polynomials." Colloquium Mathematicae 122.1 (2011): 135-138. <http://eudml.org/doc/286239>.
@article{J2011,
abstract = {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.},
author = {J. Browkin, A. Schinzel},
journal = {Colloquium Mathematicae},
keywords = {quadratic polynomials; prime factors of polynomial values},
language = {eng},
number = {1},
pages = {135-138},
title = {Prime factors of values of polynomials},
url = {http://eudml.org/doc/286239},
volume = {122},
year = {2011},
}
TY - JOUR
AU - J. Browkin
AU - A. Schinzel
TI - Prime factors of values of polynomials
JO - Colloquium Mathematicae
PY - 2011
VL - 122
IS - 1
SP - 135
EP - 138
AB - 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.
LA - eng
KW - quadratic polynomials; prime factors of polynomial values
UR - http://eudml.org/doc/286239
ER -
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