MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Japan MO Finals
2006 Japan MO Finals
3
3
Part of
2006 Japan MO Finals
Problems
(1)
Japan mathematical olympiad finals 2006, problem 3
Source:
3/3/2006
Find all functions
f
,
f,
f
,
defined on real numbers and taking real values such that
{
f
(
x
)
}
2
+
2
y
f
(
x
)
+
f
(
y
)
=
f
(
y
+
f
(
x
)
)
\left\{f(x)\right\}^2+2yf(x)+f(y)=f(y+f(x))
{
f
(
x
)
}
2
+
2
y
f
(
x
)
+
f
(
y
)
=
f
(
y
+
f
(
x
))
for all real numbers
x
,
y
.
x,y.
x
,
y
.
function
LaTeX
induction
calculus
derivative
ratio
algebra