# On polynomials that are sums of two cubes.

Revista Matemática Complutense (2007)

- Volume: 20, Issue: 1, page 207-238
- ISSN: 1139-1138

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topHooley, 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 -