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Swedish Mathematical Competition
1984 Swedish Mathematical Competition
6
6
Part of
1984 Swedish Mathematical Competition
Problems
(1)
a_i, i=1,...,7 consist of the numbers 1,...,7 ifsum 3^{a_i} = 6558
Source: 1984 Swedish Mathematical Competition p6
3/28/2021
Assume
a
1
,
a
2
,
.
.
.
,
a
14
a_1,a_2,...,a_{14}
a
1
,
a
2
,
...
,
a
14
are positive integers such that
∑
i
=
1
14
3
a
i
=
6558
\sum_{i=1}^{14}3^{a_i} = 6558
∑
i
=
1
14
3
a
i
=
6558
. Prove that the numbers
a
1
,
a
2
,
.
.
.
,
a
14
a_1,a_2,...,a_{14}
a
1
,
a
2
,
...
,
a
14
consist of the numbers
1
,
.
.
.
,
7
1,...,7
1
,
...
,
7
, each taken twice.
Sum
combinatorics
number theory