MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
2002 Canada National Olympiad
5
Functional equation
Functional equation
Source: Canada 2002
March 5, 2006
function
modular arithmetic
algebra solved
algebra
Functional Equations
Problem Statement
Let
N
=
{
0
,
1
,
2
,
…
}
\mathbb N = \{0,1,2,\ldots\}
N
=
{
0
,
1
,
2
,
…
}
. Determine all functions
f
:
N
→
N
f: \mathbb N \to \mathbb N
f
:
N
→
N
such that
x
f
(
y
)
+
y
f
(
x
)
=
(
x
+
y
)
f
(
x
2
+
y
2
)
xf(y) + yf(x) = (x+y) f(x^2+y^2)
x
f
(
y
)
+
y
f
(
x
)
=
(
x
+
y
)
f
(
x
2
+
y
2
)
for all
x
x
x
and
y
y
y
in
N
\mathbb N
N
.
Back to Problems
View on AoPS