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Argentina Contests
Argentina Team Selection Test
2007 Argentina Team Selection Test
6
6
Part of
2007 Argentina Team Selection Test
Problems
(1)
Expression with sum of digits (bounded?)
Source: Argentina IMO TST 2007 problem 6
8/27/2009
For natural
n
n
n
we define
s
(
n
)
s(n)
s
(
n
)
as the sum of digits of
n
n
n
(in base ten) Does there exist a positive real constant
c
c
c
such that for all natural
n
n
n
we have
s
(
n
)
s
(
n
2
)
≤
c
\frac{s(n)}{s(n^2)} \le c
s
(
n
2
)
s
(
n
)
≤
c
?
limit
algebra
polynomial
number theory unsolved
number theory