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Japan MO Finals
2001 Japan MO Finals
2
n is the product of one more than each digit
n is the product of one more than each digit
Source: Japanese MO Finals 2001
November 27, 2010
number theory proposed
number theory
Problem Statement
An integer
n
>
0
n>0
n
>
0
is written in decimal system as
a
m
a
m
−
1
…
a
1
‾
\overline{a_ma_{m-1}\ldots a_1}
a
m
a
m
−
1
…
a
1
. Find all
n
n
n
such that
n
=
(
a
m
+
1
)
(
a
m
−
1
+
1
)
⋯
(
a
1
+
1
)
n=(a_m+1)(a_{m-1}+1)\cdots (a_1+1)
n
=
(
a
m
+
1
)
(
a
m
−
1
+
1
)
⋯
(
a
1
+
1
)
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