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National and Regional Contests
Korea Contests
Korea National Olympiad
2006 Korea National Olympiad
1
Classic Algebra
Classic Algebra
Source: 2006 Korean National Olympiad #1
March 18, 2018
polynomial
algebra
Problem Statement
Given that for reals
a
1
,
⋯
,
a
2004
,
a_1,\cdots, a_{2004},
a
1
,
⋯
,
a
2004
,
equation
x
2006
−
2006
x
2005
+
a
2004
x
2004
+
⋯
+
a
2
x
2
+
a
1
x
+
1
=
0
x^{2006}-2006x^{2005}+a_{2004}x^{2004}+\cdots +a_2x^2+a_1x+1=0
x
2006
−
2006
x
2005
+
a
2004
x
2004
+
⋯
+
a
2
x
2
+
a
1
x
+
1
=
0
has
2006
2006
2006
positive real solution, find the maximum possible value of
a
1
.
a_1.
a
1
.
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