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Baltic Way
1993 Baltic Way
9
9
Part of
1993 Baltic Way
Problems
(1)
Another system of equations
Source: Baltic Way 1993
6/15/2012
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
.
algebra proposed
algebra