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2004 Greece National Olympiad
2
2
Part of
2004 Greece National Olympiad
Problems
(1)
There doesnt exist integers such that...
Source: Greek national M.O. 2004, Final Round,problem 2
11/15/2011
If
m
≥
2
m\geq 2
m
≥
2
show that there does not exist positive integers
x
1
,
x
2
,
.
.
.
,
x
m
,
x_1, x_2, ..., x_m,
x
1
,
x
2
,
...
,
x
m
,
such that
x
1
<
x
2
<
.
.
.
<
x
m
and
1
x
1
3
+
1
x
2
3
+
.
.
.
+
1
x
m
3
=
1.
x_1< x_2<...< x_m \ \ \text{and} \ \ \frac{1}{x_1^3}+\frac{1}{x_2^3}+...+\frac{1}{x_m^3}=1.
x
1
<
x
2
<
...
<
x
m
and
x
1
3
1
+
x
2
3
1
+
...
+
x
m
3
1
=
1.
induction
algebra unsolved
algebra