Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines
Abstract
Let a be a nonzero integer. If a is not congruent to 4 or 5 modulo 9 then there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x3+y3+z3=a. In addition, there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x3+y3+2z3=a.
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