MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
1988 Greece National Olympiad
4
\sqrt[ 2^{1453}]{2^{1821}} \in A, if 1,2 \in A and \sqrt{ab} \in A for a,b \in A
\sqrt[ 2^{1453}]{2^{1821}} \in A, if 1,2 \in A and \sqrt{ab} \in A for a,b \in A
Source: 1988 Greece MO Grade XI p4
September 7, 2024
algebra
Problem Statement
Let
A
⊆
R
A\subseteq \mathbb{R}
A
⊆
R
such that:i) If
a
,
b
∈
A
a,b\in A
a
,
b
∈
A
then
a
b
∈
A
\sqrt{ab} \in A
ab
∈
A
ii)
1
∈
A
1\in A
1
∈
A
and
2
∈
A
2\in A
2
∈
A
Prove that
2
1821
2
1453
∈
A
\sqrt[\displaystyle 2^{1453}]{2^{1821}}\in A
2
1453
2
1821
∈
A
.
Back to Problems
View on AoPS