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2008 Cuba MO
3
(m+1)/n +(n+1)/ m is integer
(m+1)/n +(n+1)/ m is integer
Source: 2008 Cuba 2.3
August 27, 2024
number theory
Integer
Problem Statement
Prove that there are infinitely many ordered pairs of positive integers
(
m
,
n
)
(m, n)
(
m
,
n
)
such that
m
+
1
n
+
n
+
1
m
\frac{m+1}{n}+\frac{n+1}{m}
n
m
+
1
+
m
n
+
1
is a positive integer.
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