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IberoAmerican
2018 lberoAmerican
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2018 lberoAmerican
Problems
(1)
Integer system of equations
Source: Iberoamerican 2018 Problem 1
9/26/2018
For each integer
n
≥
2
n \ge 2
n
≥
2
, find all integer solutions of the following system of equations:
x
1
=
(
x
2
+
x
3
+
x
4
+
.
.
.
+
x
n
)
2018
x_1 = (x_2 + x_3 + x_4 + ... + x_n)^{2018}
x
1
=
(
x
2
+
x
3
+
x
4
+
...
+
x
n
)
2018
x
2
=
(
x
1
+
x
3
+
x
4
+
.
.
.
+
x
n
)
2018
x_2 = (x_1 + x_3 + x_4 + ... + x_n)^{2018}
x
2
=
(
x
1
+
x
3
+
x
4
+
...
+
x
n
)
2018
⋮
\vdots
⋮
x
n
=
(
x
1
+
x
2
+
x
3
+
.
.
.
+
x
n
−
1
)
2018
x_n = (x_1 + x_2 + x_3 + ... + x_{n - 1})^{2018}
x
n
=
(
x
1
+
x
2
+
x
3
+
...
+
x
n
−
1
)
2018
algebra
system of equations