MathDB
Problems
Contests
National and Regional Contests
Argentina Contests
Argentina National Olympiad
2006 Argentina National Olympiad
6
6
Part of
2006 Argentina National Olympiad
Problems
(1)
a_1+a_2+... +a_n=a_1a_2 ... a_n=n
Source: Argentina 2006 OMA L3 p6
5/12/2024
We will say that a natural number
n
n
n
is adequate if there exist
n
n
n
integers
a
1
,
a
2
,
…
,
a
n
a_1,a_2,\ldots ,a_n
a
1
,
a
2
,
…
,
a
n
(which are not necessarily positive and can be repeated) such that
a
1
+
a
2
+
⋯
+
a
n
=
a
1
a
2
⋯
a
n
=
n
.
a_1+a_2+\cdots +a_n=a_1a_2 \cdots a_n=n.
a
1
+
a
2
+
⋯
+
a
n
=
a
1
a
2
⋯
a
n
=
n
.
Determine all adequate numbers.
number theory