Here $\mathbb T$ stands for the set of real transcendental numbers.
2026-04-24 11:14:01.1777029241
If $x$ is real number and $x \in \mathbb T$ is then $x^n \in \mathbb T$ for every $n \in \mathbb N$?
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If $x^n \in \Bbb A$, then $p(x^n)=0$ for some polynomial $p$ with integer coefficients. Define $f(x)=p(x^n)$. Then, $f$ is a polynomial with integer coefficients, with root $x$.