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2000 Austrian-Polish Competition
3
x_{n-1}^3 = x_n+ x_1 + 1, nxn system
x_{n-1}^3 = x_n+ x_1 + 1, nxn system
Source: Austrian - Polish 2000 APMC
May 4, 2020
algebra
system of equations
Problem Statement
For each integer
n
≥
3
n \ge 3
n
≥
3
solve in real numbers the system of equations:
{
x
1
3
=
x
2
+
x
3
+
1
.
.
.
x
n
−
1
3
=
x
n
+
x
1
+
1
x
n
3
=
x
1
+
x
2
+
1
\begin{cases} x_1^3 = x_2 + x_3 + 1 \\...\\x_{n-1}^3 = x_n+ x_1 + 1\\x_{n}^3 = x_1+ x_2 + 1 \end{cases}
⎩
⎨
⎧
x
1
3
=
x
2
+
x
3
+
1
...
x
n
−
1
3
=
x
n
+
x
1
+
1
x
n
3
=
x
1
+
x
2
+
1
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