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Chile National Olympiad
2009 Chile National Olympiad
3
sum of i/a_i = integer
sum of i/a_i = integer
Source: Chile Finals 2009 L2 p3
October 5, 2022
number theory
Sum
Problem Statement
Let
S
=
1
a
1
+
2
a
2
+
.
.
.
+
100
a
100
S = \frac{1}{a_1}+\frac{2}{a_2}+ ... +\frac{100}{a_{100}}
S
=
a
1
1
+
a
2
2
+
...
+
a
100
100
where
a
1
,
a
2
,
.
.
.
,
a
100
a_1, a_2,..., a_{100}
a
1
,
a
2
,
...
,
a
100
are positive integers. What are all the possible integer values that
S
S
S
can take ?
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