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Baltic Way
1993 Baltic Way
9
Another system of equations
Another system of equations
Source: Baltic Way 1993
June 15, 2012
algebra proposed
algebra
Problem Statement
Solve the system of equations
{
x
5
=
y
+
y
5
y
5
=
z
+
z
5
z
5
=
t
+
t
5
t
5
=
x
+
x
5
.
\begin{cases}x^5=y+y^5\\ y^5=z+z^5\\ z^5=t+t^5\\ t^5=x+x^5.\end{cases}
⎩
⎨
⎧
x
5
=
y
+
y
5
y
5
=
z
+
z
5
z
5
=
t
+
t
5
t
5
=
x
+
x
5
.
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