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2011 JBMO Shortlist
5
Really easy problem
Really easy problem
Source: JBMO 2011 Shortlist A5
May 15, 2016
number theory
Problem Statement
A5
\boxed{\text{A5}}
A5
Determine all positive integers
a
,
b
a,b
a
,
b
such that
a
2
b
2
+
208
=
4
(
[
a
,
b
]
+
(
a
,
b
)
)
2
a^{2}b^{2}+208=4([a,b]+(a,b))^2
a
2
b
2
+
208
=
4
([
a
,
b
]
+
(
a
,
b
)
)
2
where
[
a
,
b
]
[a,b]
[
a
,
b
]
-lcm of
a
,
b
a,b
a
,
b
and
(
a
,
b
)
(a,b)
(
a
,
b
)
-gcd of
a
,
b
a,b
a
,
b
.
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