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Austrian MO Beginners' Competition
2000 Austria Beginners' Competition
1
1
Part of
2000 Austria Beginners' Competition
Problems
(1)
(x-y^2)(y-x^2)+x^3+y^3=a
Source: 2000 Austria Beginners' Competition p1
10/4/2022
Let
a
a
a
be a real number. Determine, for all
a
a
a
, all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of real numbers such that
(
x
−
y
2
)
(
y
−
x
2
)
+
x
3
+
y
3
=
a
(x-y^2)(y-x^2)+x^3+y^3=a
(
x
−
y
2
)
(
y
−
x
2
)
+
x
3
+
y
3
=
a
.
algebra