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2021-IMOC qualification
N2
Fractions does not add up to get integers
Fractions does not add up to get integers
Source: 2021 IMOC qualification problems, N2
December 30, 2021
IMOC
number theory
Problem Statement
Prove: for all positive integers
m
,
n
m, n
m
,
n
1
m
+
1
m
+
1
+
⋯
+
1
m
+
n
\frac 1m + \frac 1{m+1} + \dotsb + \frac 1 {m+n}
m
1
+
m
+
1
1
+
⋯
+
m
+
n
1
is not an integer.
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