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National and Regional Contests
PEN Problems
PEN H Problems
5
5
Part of
PEN H Problems
Problems
(1)
H 5
Source:
5/25/2007
Find all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of rational numbers such that
y
2
=
x
3
ā
3
x
+
2
y^2 =x^3 -3x+2
y
2
=
x
3
ā
3
x
+
2
.
Diophantine Equations