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Baltic Way
2003 Baltic Way
20
20
Part of
2003 Baltic Way
Problems
(1)
New perfection of an integer [Baltic way 2003]
Source:
11/7/2010
Suppose that the sum of all positive divisors of a natural number
n
n
n
,
n
n
n
excluded, plus the number of these divisors is equal to
n
n
n
. Prove that
n
=
2
m
2
n = 2m^2
n
=
2
m
2
for some integer
m
m
m
.
modular arithmetic
number theory proposed
number theory