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IberoAmerican Olympiad For University Students
2005 IberoAmerican Olympiad For University Students
1
1
Part of
2005 IberoAmerican Olympiad For University Students
Problems
(1)
Degree of polynomial recursion - OIMU 2005 Problem 1
Source:
9/3/2010
Let
P
(
x
,
y
)
=
(
x
2
y
3
,
x
3
y
5
)
P(x,y)=(x^2y^3,x^3y^5)
P
(
x
,
y
)
=
(
x
2
y
3
,
x
3
y
5
)
,
P
1
=
P
P^1=P
P
1
=
P
and
P
n
+
1
=
P
∘
P
n
P^{n+1}=P\circ P^n
P
n
+
1
=
P
∘
P
n
. Also, let
p
n
(
x
)
p_n(x)
p
n
(
x
)
be the first coordinate of
P
n
(
x
,
x
)
P^n(x,x)
P
n
(
x
,
x
)
, and
f
(
n
)
f(n)
f
(
n
)
be the degree of
p
n
(
x
)
p_n(x)
p
n
(
x
)
. Find
lim
n
→
∞
f
(
n
)
1
/
n
\lim_{n\to\infty}f(n)^{1/n}
n
→
∞
lim
f
(
n
)
1/
n
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