Integral points on cubic hypersurfaces

Details Integral points on cubic hypersurfaces Integral points on cubic hypersurfaces

2006-11-03

arxiv.org/abs/math/0611086v2

Mathematics

Number Theory

18 pages

Scientific paper

Let g be a cubic polynomial with integer coefficients and n>9 variables, and
assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k.
We show that the equation g=0 has infinitely many integer solutions when the
cubic part of g defines a projective hypersurface with singular locus of
dimension

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