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Cono Sur Olympiad
2016 Cono Sur Olympiad
4
4
Part of
2016 Cono Sur Olympiad
Problems
(1)
Sum of digits equation
Source: Cono Sur Olympiad 2016, problem 4
8/28/2017
Let
S
(
n
)
S(n)
S
(
n
)
be the sum of the digits of the positive integer
n
n
n
. Find all
n
n
n
such that
S
(
n
)
(
S
(
n
)
−
1
)
=
n
−
1
S(n)(S(n)-1)=n-1
S
(
n
)
(
S
(
n
)
−
1
)
=
n
−
1
.
number theory
cono sur