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$%C. Hooley, On polynomials that are sums of two cubes, Rev. Mat. Complut. 20 (2007), no. 1, 207–238. %$

On Polynomials That Are Sums of Two Cubes
Christopher HOOLEY
Cardiff School of Mathematics
Cardiff University
Senghennydd Road
Cardiff, CF24 4AG — United Kingdom


Received: May 24, 2006
Accepted: October 4, 2006


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.

Key words: polynomials, cubes.
2000 Mathematics Subject Classification:
11D32, 11P99.