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Danube Competition in Mathematics
2016 Danube Mathematical Olympiad
1
Can The Sum Be 2016?
Can The Sum Be 2016?
Source: Mathematical Danube Competition 2016, Juniors P1
April 21, 2022
romania
algebra
Problem Statement
Let
S
=
x
1
x
2
+
x
3
x
4
+
⋯
+
x
2015
x
2016
,
S=x_1x_2+x_3x_4+\cdots+x_{2015}x_{2016},
S
=
x
1
x
2
+
x
3
x
4
+
⋯
+
x
2015
x
2016
,
where
x
1
,
x
2
,
…
,
x
2016
∈
{
3
−
2
,
3
+
2
}
.
x_1,x_2,\ldots,x_{2016}\in\{\sqrt{3}-\sqrt{2},\sqrt{3}+\sqrt{2}\}.
x
1
,
x
2
,
…
,
x
2016
∈
{
3
−
2
,
3
+
2
}
.
Can
S
S
S
be equal to
2016
?
2016?
2016
?
Cristian Lazăr
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