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We prove decidability of univariate real algebra extended with predicates forrational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in\mathbb{Z})$. Our decision procedure combines computation over real algebraiccells with the rational root theorem and witness construction via algebraicnumber density arguments.

Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers