MathDB
Problems
Contests
National and Regional Contests
Romania Contests
Romania - Local Contests
Nicolae Coculescu
2004 Nicolae Coculescu
1
a,b s.t. a³b=ba²,a²b=ba³ in group
a,b s.t. a³b=ba²,a²b=ba³ in group
Source:
December 14, 2019
group theory
Problem Statement
Let
b
,
a
b,a
b
,
a
be two elements of a group chosen such that
a
3
b
=
b
a
2
a^3b=ba^2
a
3
b
=
b
a
2
and
a
2
b
=
b
a
3
.
a^2b=ba^3.
a
2
b
=
b
a
3
.
Prove that the order of
a
a
a
divides
5.
5.
5.
Gabriel Tica
Back to Problems
View on AoPS