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Austrian-Polish
1991 Austrian-Polish Competition
2
(x^2 - 6x + 13)y = 20,(y^2 - 6y + 13)z = 20, (z^2 - 6z + 13)x = 20
(x^2 - 6x + 13)y = 20,(y^2 - 6y + 13)z = 20, (z^2 - 6z + 13)x = 20
Source: Austrian Polish 1991 APMC
April 30, 2020
system of equations
algebra
Problem Statement
Find all solutions
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
to the system
{
(
x
2
−
6
x
+
13
)
y
=
20
(
y
2
−
6
y
+
13
)
z
=
20
(
z
2
−
6
z
+
13
)
x
=
20
\begin{cases}(x^2 - 6x + 13)y = 20 \\ (y^2 - 6y + 13)z = 20 \\ (z^2 - 6z + 13)x = 20 \end{cases}
⎩
⎨
⎧
(
x
2
−
6
x
+
13
)
y
=
20
(
y
2
−
6
y
+
13
)
z
=
20
(
z
2
−
6
z
+
13
)
x
=
20
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