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Problems
Contests
National and Regional Contests
The Philippines Contests
Philippine MO
2009 Philippine MO
2
2
Part of
2009 Philippine MO
Problems
(1)
2009 Philippines MO P2
Source:
11/16/2015
(a) Find all pairs
(
n
,
x
)
(n,x)
(
n
,
x
)
of positive integers that satisfy the equation
2
n
+
1
=
x
2
2^n + 1 = x^2
2
n
+
1
=
x
2
.(b) Find all pairs
(
n
,
x
)
(n,x)
(
n
,
x
)
of positive integers that satisfy the equation
2
n
=
x
2
+
1
2^n = x^2 + 1
2
n
=
x
2
+
1
.
PMO
2009
diophantine
number theory