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arxiv: 0911.3539 · v3 · pith:BIAMM255new · submitted 2009-11-18 · 🧮 math.NT · math.AG

Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines

classification 🧮 math.NT math.AG
keywords brauer-maninexistenceintegersobstructionthereadditionaffinesbrauer
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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 x^3+y^3+z^3=a. In addition, there is no Brauer-Manin obstruction to the existence of integers x, y, z such that x^3+y^3+2z^3=a.

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