MathDB
Problems
Contests
National and Regional Contests
Thailand Contests
Thailand TST Selection Test
2017 Thailand TSTST
4
#22 functional equation
#22 functional equation
Source:
May 9, 2021
function
functional equation
algebra
Problem Statement
Find all function
f
:
N
∗
→
N
∗
f:\mathbb{N}^*\rightarrow \mathbb{N}^*
f
:
N
∗
→
N
∗
that satisfy:
(
f
(
1
)
)
3
+
(
f
(
2
)
)
3
+
.
.
.
+
(
f
(
n
)
)
3
=
(
f
(
1
)
+
f
(
2
)
+
.
.
.
+
f
(
n
)
)
2
(f(1))^3+(f(2))^3+...+(f(n))^3=(f(1)+f(2)+...+f(n))^2
(
f
(
1
)
)
3
+
(
f
(
2
)
)
3
+
...
+
(
f
(
n
)
)
3
=
(
f
(
1
)
+
f
(
2
)
+
...
+
f
(
n
)
)
2
Back to Problems
View on AoPS