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2023 APMO
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2
Part of
2023 APMO
Problems
(1)
APMO Number Theory
Source: APMO 2023 Problem 2
7/5/2023
Find all integers
n
n
n
satisfying
n
≥
2
n \geq 2
n
≥
2
and
σ
(
n
)
p
(
n
)
−
1
=
n
\dfrac{\sigma(n)}{p(n)-1} = n
p
(
n
)
−
1
σ
(
n
)
=
n
, in which
σ
(
n
)
\sigma(n)
σ
(
n
)
denotes the sum of all positive divisors of
n
n
n
, and
p
(
n
)
p(n)
p
(
n
)
denotes the largest prime divisor of
n
n
n
.
number theory
APMO
APMO 2023