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International Contests
IMO Longlists
1986 IMO Longlists
55
Determine all n-digit numbers
Determine all n-digit numbers
Source:
August 29, 2010
number theory unsolved
number theory
Problem Statement
Given an integer
n
≥
2
n \geq 2
n
≥
2
, determine all
n
n
n
-digit numbers
M
0
=
a
1
a
2
⋯
a
n
‾
(
a
i
≠
0
,
i
=
1
,
2
,
.
.
.
,
n
)
M_0 = \overline{a_1a_2 \cdots a_n} \ (a_i \neq 0, i = 1, 2, . . ., n)
M
0
=
a
1
a
2
⋯
a
n
(
a
i
=
0
,
i
=
1
,
2
,
...
,
n
)
divisible by the numbers
M
1
=
a
2
a
3
⋯
a
n
a
1
‾
M_1 = \overline{a_2a_3 \cdots a_na_1}
M
1
=
a
2
a
3
⋯
a
n
a
1
,
M
2
=
a
3
a
4
⋯
a
n
a
1
a
2
‾
M_2 = \overline{a_3a_4 \cdots a_na_1 a_2}
M
2
=
a
3
a
4
⋯
a
n
a
1
a
2
,
⋯
\cdots
⋯
,
M
n
−
1
=
a
n
a
1
a
2
.
.
.
a
n
−
1
‾
.
M_{n-1} = \overline{a_na_1a_2 . . .a_{n-1}}.
M
n
−
1
=
a
n
a
1
a
2
...
a
n
−
1
.
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