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2020 Argentina National Olympiad
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1
Part of
2020 Argentina National Olympiad
Problems
(1)
171-digit no, 7 divides both S (n) and S (n + 1), sum of digits
Source: 2020 Argentina OMA L3 p1
12/26/2020
For every positive integer
n
n
n
, let
S
(
n
)
S (n)
S
(
n
)
be the sum of the digits of
n
n
n
. Find, if any, a
171
171
171
-digit positive integer
n
n
n
such that
7
7
7
divides
S
(
n
)
S (n)
S
(
n
)
and
7
7
7
divides
S
(
n
+
1
)
S (n + 1)
S
(
n
+
1
)
.
number theory
divides
sum of digits