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India STEMS
2021 India STEMS
STEMS 2021 Math Cat C
Q2
Q2
Part of
STEMS 2021 Math Cat C
Problems
(1)
Number field having infinitely many roots
Source: own; STEMS 2021 CAT C p2
1/24/2021
Does there exist a nonzero algebraic number
α
\alpha
α
with
∣
α
∣
≠
1
|\alpha| \neq 1
∣
α
∣
=
1
such that there exists infinitely many positive integers
n
n
n
for which there's
β
n
∈
C
\beta_n \in \mathbb{C}
β
n
∈
C
with
β
n
∈
Q
(
α
)
\beta_n \in \mathbb{Q}(\alpha)
β
n
∈
Q
(
α
)
and
β
n
n
=
α
\beta_n^n = \alpha
β
n
n
=
α
?
Algebraic Number Theory
number theory