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Bulgarian National Mathematical Olympiad 2016,problem 1
Bulgarian National Mathematical Olympiad 2016,problem 1
Source:
June 22, 2017
number theory
Problem Statement
Find all positive integers
m
m
m
and
n
n
n
such that
(
2
2
n
+
1
)
(
2
2
m
+
1
)
(2^{2^{n}}+1)(2^{2^{m}}+1)
(
2
2
n
+
1
)
(
2
2
m
+
1
)
is divisible by
m
ā
n
m\cdot n
m
ā
n
.
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