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2020 Japan MO Finals
1
Japan MO Finals 2020-1
Japan MO Finals 2020-1
Source: Japan MO Finals 2020-1
February 11, 2020
Japan
number theory
Problem Statement
Find all pairs of positive integers
(
m
,
n
)
(m,n)
(
m
,
n
)
such that
n
2
+
1
2
m
\frac{n^2+1}{2m}
2
m
n
2
+
1
and
2
n
−
1
+
m
+
4
\sqrt{2^{n-1}+m+4}
2
n
−
1
+
m
+
4
are both integers.
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