MathDB
Problems
Contests
International Contests
Baltic Way
2009 Baltic Way
5
5
Part of
2009 Baltic Way
Problems
(1)
equation
Source: Baltic Way 2009
11/12/2009
Let
f
0
=
f
1
=
1
f_0=f_1=1
f
0
=
f
1
=
1
and
f
i
+
2
=
f
i
+
1
+
f
i
f_{i+2}=f_{i+1}+f_i
f
i
+
2
=
f
i
+
1
+
f
i
for all
n
≥
0
n\ge 0
n
≥
0
. Find all real solutions to the equation
x
2010
=
f
2009
⋅
x
+
f
2008
x^{2010}=f_{2009}\cdot x+f_{2008}
x
2010
=
f
2009
⋅
x
+
f
2008
function
algebra proposed
algebra