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2022 Turkey MO (2nd round)
4
4
Part of
2022 Turkey MO (2nd round)
Problems
(1)
An easy 3 variable equation
Source: Turkey National Mathematical Olympiad 2022 P4
12/23/2022
For which real numbers
a
a
a
, there exist pairwise different real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
satisfying
x
3
+
a
y
+
z
=
y
3
+
a
x
+
z
=
z
3
+
a
x
+
y
=
−
3.
\frac{x^3+a}{y+z}=\frac{y^3+a}{x+z}=\frac{z^3+a}{x+y}= -3.
y
+
z
x
3
+
a
=
x
+
z
y
3
+
a
=
x
+
y
z
3
+
a
=
−
3.
Diophantine equation
number theory