Chapter

Diophantine Equations and Inequalities in Algebraic Number Fields

pp 111-126

Small Nonnegative Solutions of Additive Equations

  • Wang YuanAffiliated withInstitute of Mathematics, Academia Sinica

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Abstract

Let α1…,α2s be 2s nonzero elements of P. Consider the additive equation of the type
$$ {\alpha _1}\lambda _1^k + \cdots + {\alpha _s}\lambda _s^k - {\alpha _{s + 1}}\lambda _{s + 1}^k - \cdots - {\alpha _{2s}}\lambda _{2s}^k = 0. $$
(9.1)