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IberoAmerican
2014 IberoAmerican
1
Same sum of digits between multiples
Same sum of digits between multiples
Source:
September 24, 2014
number theory unsolved
number theory
Problem Statement
For each positive integer
n
n
n
, let
s
(
n
)
s(n)
s
(
n
)
be the sum of the digits of
n
n
n
. Find the smallest positive integer
k
k
k
such that
s
(
k
)
=
s
(
2
k
)
=
s
(
3
k
)
=
⋯
=
s
(
2013
k
)
=
s
(
2014
k
)
.
s(k) = s(2k) = s(3k) = \cdots = s(2013k) = s(2014k).
s
(
k
)
=
s
(
2
k
)
=
s
(
3
k
)
=
⋯
=
s
(
2013
k
)
=
s
(
2014
k
)
.
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