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Mexico Contests
Mexico National Olympiad
1998 Mexico National Olympiad
4
4
Part of
1998 Mexico National Olympiad
Problems
(1)
integers in form 1/a_1+2/a_2+...+9/a_9, where a_i digits
Source: Mexican Mathematical Olympiad 1998 P4
7/28/2018
Find all integers that can be written in the form
1
a
1
+
2
a
2
+
.
.
.
+
9
a
9
\frac{1}{a_1}+\frac{2}{a_2}+...+\frac{9}{a_9}
a
1
1
+
a
2
2
+
...
+
a
9
9
where
a
1
,
a
2
,
.
.
.
,
a
9
a_1,a_2, ...,a_9
a
1
,
a
2
,
...
,
a
9
are nonzero digits, not necessarily different.
number theory
Integers