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International Contests
APMO
2002 APMO
5
5
Part of
2002 APMO
Problems
(1)
Functional equation
Source: APMO 2002
4/8/2006
Let
R
{\bf R}
R
denote the set of all real numbers. Find all functions
f
f
f
from
R
{\bf R}
R
to
R
{\bf R}
R
satisfying: (i) there are only finitely many
s
s
s
in
R
{\bf R}
R
such that
f
(
s
)
=
0
f(s)=0
f
(
s
)
=
0
, and (ii)
f
(
x
4
+
y
)
=
x
3
f
(
x
)
+
f
(
f
(
y
)
)
f(x^4+y)=x^3f(x)+f(f(y))
f
(
x
4
+
y
)
=
x
3
f
(
x
)
+
f
(
f
(
y
))
for all
x
,
y
x,y
x
,
y
in
R
{\bf R}
R
.
function
induction
algebra unsolved
algebra