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Baltic Way
2005 Baltic Way
20
20
Part of
2005 Baltic Way
Problems
(1)
Find all positive integers
Source: Baltic way 2005/20
11/8/2005
Find all positive integers
n
=
p
1
p
2
⋯
p
k
n=p_1p_2 \cdots p_k
n
=
p
1
p
2
⋯
p
k
which divide
(
p
1
+
1
)
(
p
2
+
1
)
⋯
(
p
k
+
1
)
(p_1+1)(p_2+1)\cdots (p_k+1)
(
p
1
+
1
)
(
p
2
+
1
)
⋯
(
p
k
+
1
)
where
p
1
p
2
⋯
p
k
p_1 p_2 \cdots p_k
p
1
p
2
⋯
p
k
is the factorization of
n
n
n
into prime factors (not necessarily all distinct).
number theory proposed
number theory