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Bulgaria National Olympiad
1964 Bulgaria National Olympiad
Problem 2
system in n variables, R (Bulgaria 1964 P2)
system in n variables, R (Bulgaria 1964 P2)
Source:
June 24, 2021
Problem Statement
Find all
n
n
n
-tuples of reals
x
1
,
x
2
,
…
,
x
n
x_1,x_2,\ldots,x_n
x
1
,
x
2
,
…
,
x
n
satisfying the system:
{
x
1
x
2
⋯
x
n
=
1
x
1
−
x
2
x
3
⋯
x
n
=
1
x
1
x
2
−
x
3
x
4
⋯
x
n
=
1
⋮
x
1
x
2
⋯
x
n
−
1
−
x
n
=
1
\begin{cases}x_1x_2\cdots x_n=1\\x_1-x_2x_3\cdots x_n=1\\x_1x_2-x_3x_4\cdots x_n=1\\\vdots\\x_1x_2\cdots x_{n-1}-x_n=1\end{cases}
⎩
⎨
⎧
x
1
x
2
⋯
x
n
=
1
x
1
−
x
2
x
3
⋯
x
n
=
1
x
1
x
2
−
x
3
x
4
⋯
x
n
=
1
⋮
x
1
x
2
⋯
x
n
−
1
−
x
n
=
1
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