On polynomials that are sums of two cubes.

Hooley, Christopher. "On polynomials that are sums of two cubes.." Revista Matemática Complutense 20.1 (2007): 207-238. <http://eudml.org/doc/41932>.

@article{Hooley2007,
abstract = {It is proved that, if F(x) be a cubic polynomial with integral coefficients having the property that F(n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F(x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F(n) is merely assumed to be a sum of two integral cubes of either sign. It is deduced that analogous propositions are true for cubic polynomials F(x0, ..., xr) in more than one indeterminate.},
author = {Hooley, Christopher},
journal = {Revista Matemática Complutense},
keywords = {Polinomios; Ecuaciones diofánticas; Teoría aditiva de números; cubic polynomial; sum of two cubes},
language = {eng},
number = {1},
pages = {207-238},
title = {On polynomials that are sums of two cubes.},
url = {http://eudml.org/doc/41932},
volume = {20},
year = {2007},
}

TY - JOUR
AU - Hooley, Christopher
TI - On polynomials that are sums of two cubes.
JO - Revista Matemática Complutense
PY - 2007
VL - 20
IS - 1
SP - 207
EP - 238
AB - It is proved that, if F(x) be a cubic polynomial with integral coefficients having the property that F(n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F(x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F(n) is merely assumed to be a sum of two integral cubes of either sign. It is deduced that analogous propositions are true for cubic polynomials F(x0, ..., xr) in more than one indeterminate.
LA - eng
KW - Polinomios; Ecuaciones diofánticas; Teoría aditiva de números; cubic polynomial; sum of two cubes
UR - http://eudml.org/doc/41932
ER -