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National and Regional Contests
China Contests
China Western Mathematical Olympiad
2017 China Western Mathematical Olympiad
2
2
Part of
2017 China Western Mathematical Olympiad
Problems
(1)
Find greatest value of n
Source: CWMI 2017 Q2
8/14/2017
Let
n
n
n
be a positive integer such that there exist positive integers
x
1
,
x
2
,
⋯
,
x
n
x_1,x_2,\cdots ,x_n
x
1
,
x
2
,
⋯
,
x
n
satisfying
x
1
x
2
⋯
x
n
(
x
1
+
x
2
+
⋯
+
x
n
)
=
100
n
.
x_1x_2\cdots x_n(x_1 + x_2 + \cdots + x_n)=100n.
x
1
x
2
⋯
x
n
(
x
1
+
x
2
+
⋯
+
x
n
)
=
100
n
.
Find the greatest possible value of
n
n
n
.
algebra