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2022 Malaysia IMONST 2
2
Given n integers, sum = 0, product = n, find all n.
Given n integers, sum = 0, product = n, find all n.
Source: IMONST2 2022 Senior #2
July 4, 2023
algebra
Problem Statement
It is known that there are
n
n
n
integers
a
1
,
a
2
,
⋯
,
a
n
a_1, a_2, \cdots, a_n
a
1
,
a
2
,
⋯
,
a
n
such that
a
1
+
a
2
+
⋯
+
a
n
=
0
and
a
1
×
a
2
×
⋯
×
a
n
=
n
.
a_1 + a_2 + \cdots + a_n = 0 \qquad \text{and} \qquad a_1 \times a_2 \times \cdots \times a_n = n.
a
1
+
a
2
+
⋯
+
a
n
=
0
and
a
1
×
a
2
×
⋯
×
a
n
=
n
.
Determine all possible values of
n
n
n
.
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