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Polish MO Finals
1981 Polish MO Finals
5
x^3 +x^2y+xy^2 +y^3 = 8(x^2 +xy+y^2 +1) NT
x^3 +x^2y+xy^2 +y^3 = 8(x^2 +xy+y^2 +1) NT
Source: Polish MO Finals 1981 p5
August 24, 2024
number theory
diophantine
Problem Statement
Determine all pairs of integers
(
x
,
y
)
(x,y)
(
x
,
y
)
satisfying the equation
x
3
+
x
2
y
+
x
y
2
+
y
3
=
8
(
x
2
+
x
y
+
y
2
+
1
)
.
x^3 +x^2y+xy^2 +y^3 = 8(x^2 +xy+y^2 +1).
x
3
+
x
2
y
+
x
y
2
+
y
3
=
8
(
x
2
+
x
y
+
y
2
+
1
)
.
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