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Contests
National and Regional Contests
PEN Problems
PEN H Problems
7
7
Part of
PEN H Problems
Problems
(1)
H 7
Source:
5/25/2007
Determine all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of positive integers satisfying the equation
(
x
+
y
)
2
ā
2
(
x
y
)
2
=
1.
(x+y)^{2}-2(xy)^{2}=1.
(
x
+
y
)
2
ā
2
(
x
y
)
2
=
1.
Diophantine Equations