10.46298/hrj.2006.153
https://hrj.episciences.org/153
Hooley, C
C
Hooley
On polynomials that equal binary cubic forms.
Let $F(x)$ be a cubic polynomial with rational integral coefficients with the property that, for all sufficiently large integers $n,\,F(n)$ is equal to a value assumed, through integers $u, v$, by a given irreducible binary cubic form $f(u,v)=au^3+bu^2v+cuv^2+dv^3$ with rational integral coefficients. We prove that then $F(x)=f(u(x),v(x))$, where $u=u(x), v=v(x)$ are linear binomials in $x$.
episciences.org
Chebotarev's theorem
incongruent integers
perfect square
binary cubic forms
[MATH] Mathematics [math]
2015-06-12
2006-01-01
2006-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01111461v1
2804-7370
https://hrj.episciences.org/153/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 29 - 2006
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