An improved bound on sums of square roots via the subspace theorem

Friedrich Eisenbrand, Matthieu Haeberle, Neta Singer

The sum of square roots is as follows: Given $x_1,\dots ,x_n\in \mathbb{Z}$ and $a_1,\dots ,a_n\in \mathbb{N}$ decide whether $E={\sum }_{i=1}^n{x}_i\sqrt{a_i}\ge 0$. It is a promi…