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Problems
Contests
National and Regional Contests
Poland Contests
Polish MO Finals
1997 Polish MO Finals
1
find x_7
find x_7
Source:
November 11, 2005
number theory unsolved
number theory
Problem Statement
The positive integers
x
1
,
x
2
,
.
.
.
,
x
7
x_1, x_2, ... , x_7
x
1
,
x
2
,
...
,
x
7
satisfy
x
6
=
144
x_6 = 144
x
6
=
144
,
x
n
+
3
=
x
n
+
2
(
x
n
+
1
+
x
n
)
x_{n+3} = x_{n+2}(x_{n+1}+x_n)
x
n
+
3
=
x
n
+
2
(
x
n
+
1
+
x
n
)
for
n
=
1
,
2
,
3
,
4
n = 1, 2, 3, 4
n
=
1
,
2
,
3
,
4
. Find
x
7
x_7
x
7
.
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