We prove that for every quadratic binomial
$f(x)=rx^2+s\in{\mathbb Z}[x]$
there are pairs $\langle a,b\rangle\in{\mathbb N}^2$ such that $a\ne 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 ${\mathbb Z}.$
Keywords:
prove every quadratic binomial mathbb there pairs langle rangle mathbb have prime factors min arbitrarily large prove result every monic quadratic trinomial nbsp mathbb
Affiliations des auteurs :
J. Browkin
1
;
A. Schinzel
1
1
Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
@article{10_4064_cm122_1_12,
author = {J. Browkin and A. Schinzel},
title = {Prime factors of values of polynomials},
journal = {Colloquium Mathematicum},
pages = {135--138},
year = {2011},
volume = {122},
number = {1},
doi = {10.4064/cm122-1-12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-12/}
}
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AU - J. Browkin
AU - A. Schinzel
TI - Prime factors of values of polynomials
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PY - 2011
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J. Browkin; A. Schinzel. Prime factors of values of polynomials. Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 135-138. doi: 10.4064/cm122-1-12
