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2023 NMTC Junior
P7
P7
Part of
2023 NMTC Junior
Problems
(1)
NMTC Junior 2023 P7
Source: NMTC Junior 2023 P7
11/8/2023
Let
n
n
n
be a positive integer; and
S
(
n
)
S(n)
S
(
n
)
denote the sum of all digits in the decimal representation of
n
n
n
. A positive integer obtained by removing one or several digits from the right hand end of the decimal representation of
n
n
n
is called the truncation of
n
n
n
. The sum of all truncations of
n
n
n
is denoted as
T
(
n
)
T(n)
T
(
n
)
. Prove that
S
(
n
)
+
9
T
(
n
)
=
n
S(n)+9T(n)=n
S
(
n
)
+
9
T
(
n
)
=
n
number theory
nmtc