MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
34
34
Part of
PEN A Problems
Problems
(1)
A 34
Source:
5/25/2007
Let
p
1
,
p
2
,
⋯
,
p
n
p_{1}, p_{2}, \cdots, p_{n}
p
1
,
p
2
,
⋯
,
p
n
be distinct primes greater than
3
3
3
. Show that
2
p
1
p
2
⋯
p
n
+
1
2^{p_{1}p_{2}\cdots p_{n}}+1
2
p
1
p
2
⋯
p
n
+
1
has at least
4
n
4^{n}
4
n
divisors.
Divisibility Theory