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Lusophon Mathematical Olympiad
2018 Lusophon Mathematical Olympiad
3
3
Part of
2018 Lusophon Mathematical Olympiad
Problems
(1)
smallest a so that S(n)-S(n+a) = 2018, where S(n)=sum of digits
Source: Lusophon 2018 CPLP P3
9/13/2018
For each positive integer
n
n
n
, let
S
(
n
)
S(n)
S
(
n
)
be the sum of the digits of
n
n
n
. Determines the smallest positive integer
a
a
a
such that there are infinite positive integers
n
n
n
for which you have
S
(
n
)
ā
S
(
n
+
a
)
=
2018
S (n) -S (n + a) = 2018
S
(
n
)
ā
S
(
n
+
a
)
=
2018
.
number theory
sum of digits
minimum