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2003 German National Olympiad
5
Interesting number theory problem
Interesting number theory problem
Source: German math olympiad
March 22, 2020
number theory
national olympiad
Problem Statement
n
n
n
is a positive integer. Let
a
(
n
)
a(n)
a
(
n
)
be the smallest number for which
n
∣
a
(
n
)
!
n\mid a(n)!
n
∣
a
(
n
)!
Find all solutions of:
a
(
n
)
n
=
2
3
\frac{a(n)}{n}=\frac{2}{3}
n
a
(
n
)
=
3
2
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