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Hungary Contests
Kürschák Math Competition
1989 Kurschak Competition
2
2
Part of
1989 Kurschak Competition
Problems
(1)
Multiples of M have the same digital sum
Source: Kürschák 1989, problem 2
7/20/2014
For any positive integer
n
n
n
denote
S
(
n
)
S(n)
S
(
n
)
the digital sum of
n
n
n
when represented in the decimal system. Find every positive integer
M
M
M
for which
S
(
M
k
)
=
S
(
M
)
S(Mk)=S(M)
S
(
M
k
)
=
S
(
M
)
holds for all integers
1
≤
k
≤
M
1\le k\le M
1
≤
k
≤
M
.
number theory unsolved
number theory