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Danube Competition in Mathematics
2013 Danube Mathematical Competition
1
Sum x_i = Sum 1/xi =0, from i=1 to n, find n
Sum x_i = Sum 1/xi =0, from i=1 to n, find n
Source: Danube 2013 junior p1
July 22, 2019
algebra
Sum
reciprocal sum
Problem Statement
Determine the natural numbers
n
≥
2
n\ge 2
n
≥
2
for which exist
x
1
,
x
2
,
.
.
.
,
x
n
∈
R
∗
x_1,x_2,...,x_n \in R^*
x
1
,
x
2
,
...
,
x
n
∈
R
∗
, such that
x
1
+
x
2
+
.
.
.
+
x
n
=
1
x
1
+
1
x
2
+
.
.
.
+
1
x
n
=
0
x_1+x_2+...+x_n=\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}=0
x
1
+
x
2
+
...
+
x
n
=
x
1
1
+
x
2
1
+
...
+
x
n
1
=
0
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