The Diophantine problem for systems of algebraic equations with exponents

Richard Mandel, Alexander Ushakov

Consider the equation $q_1{\alpha }^{x_1}+\cdots +q_k{\alpha }^{x_k}=q$, with constants $\alpha \in \overline{\mathbb{Q}}\setminus \{0,1\}$, $q_1,\dots ,q_k,q\in \overline{\mathbb{Q}}$ and unknowns $x_1…