Geodesic
Prime factors of values of polynomials
J. Browkin 1   ; A. Schinzel 1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
Colloquium Mathematicum, Tome 122 (2011) no. 1, pp. 135-138 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\mathbb Z}.$
DOI : 10.4064/cm122-1-12
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

J. Browkin  1   ; A. Schinzel  1

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

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