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Sweden Contests
Swedish Mathematical Competition
1981 Swedish Mathematical Competition
2
2
Part of
1981 Swedish Mathematical Competition
Problems
(1)
3x3 system, x^y = z , y^z = x, z^x = y
Source: 1981 Swedish Mathematical Competition p2
3/28/2021
Does
{
x
y
=
z
y
z
=
x
z
x
=
y
\left\{ \begin{array}{l} x^y = z \\ y^z = x \\ z^x = y \\ \end{array} \right.
⎩
⎨
⎧
x
y
=
z
y
z
=
x
z
x
=
y
have any solutions in positive reals apart from
x
=
y
=
z
=
1
x = y = z= 1
x
=
y
=
z
=
1
?
system of equations
System
algebra