MathDB
Problems
Contests
International Contests
IMO Longlists
1977 IMO Longlists
35
35
Part of
1977 IMO Longlists
Problems
(1)
Mutliplying by 9 reverses digits [ILL 1977]
Source:
1/11/2011
Find all numbers
N
=
a
1
a
2
…
a
n
‾
N=\overline{a_1a_2\ldots a_n}
N
=
a
1
a
2
…
a
n
for which
9
×
a
1
a
2
…
a
n
‾
=
a
n
…
a
2
a
1
‾
9\times \overline{a_1a_2\ldots a_n}=\overline{a_n\ldots a_2a_1}
9
×
a
1
a
2
…
a
n
=
a
n
…
a
2
a
1
such that at most one of the digits
a
1
,
a
2
,
…
,
a
n
a_1,a_2,\ldots ,a_n
a
1
,
a
2
,
…
,
a
n
is zero.
induction
number theory unsolved
number theory