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2012 Cuba MO
1
x_{1006} =? x_1+x_2+...+x_{1006} = 503^2
x_{1006} =? x_1+x_2+...+x_{1006} = 503^2
Source: 2012 Cuba MO 2.1
September 18, 2024
algebra
system of equations
Problem Statement
If
x
1
x
1
+
1
=
x
2
x
2
+
3
=
x
3
x
3
+
5
=
.
.
.
=
x
1006
x
1006
+
2011
\frac{x_1}{x_1+1} = \frac{x_2}{x_2+3} = \frac{x_3}{x_3+5} = ...= \frac{x_{1006}}{x_{1006}+2011}
x
1
+
1
x
1
=
x
2
+
3
x
2
=
x
3
+
5
x
3
=
...
=
x
1006
+
2011
x
1006
and
x
1
+
x
2
+
.
.
.
+
x
1006
=
50
3
2
x_1+x_2+...+x_{1006} = 503^2
x
1
+
x
2
+
...
+
x
1006
=
50
3
2
, determine the value of
x
1006
x_{1006}
x
1006
.
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