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National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine National Mathematical Olympiad
2021 Ukraine National Mathematical Olympiad
10.8
10.8
Part of
2021 Ukraine National Mathematical Olympiad
Problems
(1)
\phi (n)+1 (not necessarily different) divisors n with the sum n
Source: 2021 Ukraine NMO 10.8 11.7
4/4/2021
Given a natural number
n
n
n
. Prove that you can choose
ϕ
(
n
)
+
1
\phi (n)+1
ϕ
(
n
)
+
1
(not necessarily different) divisors
n
n
n
with the sum
n
n
n
. Here
ϕ
(
n
)
\phi (n)
ϕ
(
n
)
denotes the number of natural numbers less than
n
n
n
that are coprime with
n
n
n
.(Fedir Yudin)
number theory
Divisors