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Junior Balkan MO
2006 Junior Balkan MO
3
3
Part of
2006 Junior Balkan MO
Problems
(1)
Sum of divisors is 2n
Source: JBMO 2006
6/29/2006
We call a number perfect if the sum of its positive integer divisors(including
1
1
1
and
n
n
n
) equals
2
n
2n
2
n
. Determine all perfect numbers
n
n
n
for which
n
ā
1
n-1
n
ā
1
and
n
+
1
n+1
n
+
1
are prime numbers.
number theory unsolved
number theory