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Romanian Masters of Mathematics Collection
2017 Romanian Master of Mathematics Shortlist
N1
Sum of Digits
Sum of Digits
Source:
June 10, 2018
sum of digits
number theory
Problem Statement
For each positive integer
k
k
k
, let
S
(
k
)
S(k)
S
(
k
)
the sum of digits of
k
k
k
in decimal system. Show that there is an integer
k
k
k
, with no
9
9
9
in it's decimal representation, such that:
S
(
2
2
4
2017
k
)
=
S
(
k
)
S(2^{24^{2017}}k)=S(k)
S
(
2
2
4
2017
k
)
=
S
(
k
)
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