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.
@article{urn:eudml:doc:41932,
title = {On polynomials that are sums of two cubes.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {20},
year = {2007},
pages = {207-238},
mrnumber = {MR2310584},
zbl = {1136.11060},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41932}
}
Hooley, Christopher. On polynomials that are sums of two cubes.. Revista Matemática de la Universidad Complutense de Madrid, Tome 20 (2007) pp. 207-238. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41932/