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All-Russian Olympiad Regional Round
1997 All-Russian Olympiad Regional Round
11.3
11.3
Part of
1997 All-Russian Olympiad Regional Round
Problems
(1)
sum of digits S(3^n) >= S(3^{n+1})- All-Russian MO 1997 Regional (R4) 11.3
Source:
9/24/2024
Let us denote by
S
(
m
)
S(m)
S
(
m
)
the sum of the digits of the natural number
m
m
m
. Prove that there are infinitely many positive integers
n
n
n
such that
S
(
3
n
)
≥
S
(
3
n
+
1
)
.
S(3^n) \ge S(3^{n+1}).
S
(
3
n
)
≥
S
(
3
n
+
1
)
.
number theory
sum of digits