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Balkan MO Shortlist
2016 Balkan MO Shortlist
N1
N1
Part of
2016 Balkan MO Shortlist
Problems
(1)
1^{\phi (n)} + 2^{\phi (n)} +... + n^{\phi (n)} coprime with n
Source: Balkan BMO Shortlist 2016 N1
7/30/2019
Find all natural numbers
n
n
n
for which
1
ϕ
(
n
)
+
2
ϕ
(
n
)
+
.
.
.
+
n
ϕ
(
n
)
1^{\phi (n)} + 2^{\phi (n)} +... + n^{\phi (n)}
1
ϕ
(
n
)
+
2
ϕ
(
n
)
+
...
+
n
ϕ
(
n
)
is coprime with
n
n
n
.
coprime
phi function
number theory
IMO Shortlist