MathDB

Number field having infinitely many roots

Source: own; STEMS 2021 CAT C p2

January 24, 2021

Algebraic Number Theorynumber theory

Problem Statement

Does there exist a nonzero algebraic number

\alpha

with

|\alpha| \neq 1

such that there exists infinitely many positive integers

n

for which there's

\beta_n \in \mathbb{C}

with

\beta_n \in \mathbb{Q}(\alpha)

and

\beta_n^n = \alpha