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Official Ukraine Selection Cycle
Ukraine Team Selection Test
1999 Ukraine Team Selection Test
10
10
Part of
1999 Ukraine Team Selection Test
Problems
(1)
2^{w(n)} \le k\sqrt[4]{n}. no of (positive) prime divisors related inequality
Source: Ukrainian TST 1999 p10
2/13/2020
For a natural number
n
n
n
, let
w
(
n
)
w(n)
w
(
n
)
denote the number of (positive) prime divisors of
n
n
n
. Find the smallest positive integer
k
k
k
such that
2
w
(
n
)
≤
k
n
4
2^{w(n)} \le k \sqrt[4]{ n}
2
w
(
n
)
≤
k
4
n
for each
n
∈
N
n \in N
n
∈
N
.
number theory
prime divisors
inequalities
min