Resumen de On polynomials that are sums of two cubes

Christopher Hooley

• 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.