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2021-IMOC qualification
N2
N2
Part of
2021-IMOC qualification
Problems
(1)
Fractions does not add up to get integers
Source: 2021 IMOC qualification problems, N2
12/30/2021
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.
IMOC
number theory