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18
The sum 1/(1+a) + 1/(1+2a) + ... + 1/(1+na) isn't an integer
The sum 1/(1+a) + 1/(1+2a) + ... + 1/(1+na) isn't an integer
Source: IMO LongList 1979 - P18
June 1, 2011
number theory proposed
number theory
Problem Statement
Show that for no integers
a
≥
1
,
n
≥
1
a \geq 1, n \geq 1
a
≥
1
,
n
≥
1
is the sum
1
+
1
1
+
a
+
1
1
+
2
a
+
⋯
+
1
1
+
n
a
1+\frac{1}{1+a}+\frac{1}{1+2a}+\cdots+\frac{1}{1+na}
1
+
1
+
a
1
+
1
+
2
a
1
+
⋯
+
1
+
na
1
an integer.
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