MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2015 Latvia Baltic Way TST
15
15
Part of
2015 Latvia Baltic Way TST
Problems
(1)
w(n) < w(n + 1) < w(n + 2), no of different primes that divide n
Source: 2015 Latvia BW TST P15
12/16/2022
Let
w
(
n
)
w (n)
w
(
n
)
denote the number of different prime numbers by which
n
n
n
is divisible. Prove that there are infinitely many natural numbers
n
n
n
such that
w
(
n
)
<
w
(
n
+
1
)
<
w
(
n
+
2
)
w(n) < w(n + 1) < w(n + 2)
w
(
n
)
<
w
(
n
+
1
)
<
w
(
n
+
2
)
.
number theory
Divisors
prime divisor
prime divisors