MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
61
61
Part of
PEN A Problems
Problems
(1)
A 61
Source:
5/25/2007
For any positive integer
n
>
1
n>1
n
>
1
, let
p
(
n
)
p(n)
p
(
n
)
be the greatest prime divisor of
n
n
n
. Prove that there are infinitely many positive integers
n
n
n
with
p
(
n
)
<
p
(
n
+
1
)
<
p
(
n
+
2
)
.
p(n)<p(n+1)<p(n+2).
p
(
n
)
<
p
(
n
+
1
)
<
p
(
n
+
2
)
.
search
Divisibility Theory