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Paraguay Mathematical Olympiad
2006 Paraguay Mathematical Olympiad
4
Problem 4
Problem 4
Source: Paraguayan Mathematical Olympiad 2006
July 22, 2015
number theory
Problem Statement
Consider all pairs of positive integers
(
a
,
b
)
(a,b)
(
a
,
b
)
, with
a
<
b
a<b
a
<
b
, such that
a
+
b
=
2
,
160
\sqrt{a} +\sqrt{b} = \sqrt{2,160}
a
+
b
=
2
,
160
Determine all possible values of
a
a
a
.
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