MathDB
Problems
Contests
International Contests
Balkan MO Shortlist
2013 Balkan MO Shortlist
N9
N9
Part of
2013 Balkan MO Shortlist
Problems
(1)
x_1^{x_2}=x_2^{x_3}=...=x_{n-1}^{x_n}=x_n^{x_1} solve in Q+
Source: Balkan MO Shortlist 2013 N9 BMO
3/10/2020
Let
n
≥
2
n\ge 2
n
≥
2
be a given integer. Determine all sequences
x
1
,
.
.
.
,
x
n
x_1,...,x_n
x
1
,
...
,
x
n
of positive rational numbers such that
x
1
x
2
=
x
2
x
3
=
.
.
.
=
x
n
−
1
x
n
=
x
n
x
1
x_1^{x_2}=x_2^{x_3}=...=x_{n-1}^{x_n}=x_n^{x_1}
x
1
x
2
=
x
2
x
3
=
...
=
x
n
−
1
x
n
=
x
n
x
1
number theory
rational