Abstract

In this master thesis, we study Diophantine inequalities. Our aim is to solve inequalities involving polynomials with arbitrary real coefficients, where the ratio of two coefficients is irrational. In 1929, it was conjectured by Oppenheim that the inequality |\alpha_1x_1^2 + \ldots + \alpha_nx_n^2|<\delta, provided n \geq 5, \alpha_1,\ldots,\alpha_n\in\R, not all
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