Prime factors of values of polynomials
Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 135-138
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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
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author = {J. Browkin and A. Schinzel},
title = {Prime factors of values of polynomials},
journal = {Colloquium Mathematicum},
pages = {135--138},
publisher = {mathdoc},
volume = {122},
number = {1},
year = {2011},
doi = {10.4064/cm122-1-12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm122-1-12/}
}
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
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