MathDB
Problems
Contests
International Contests
IberoAmerican
2023 Iberoamerican
2
Functional on Integers
Functional on Integers
Source: IberoAmerican 2023, Day 1, P2
September 8, 2023
functional equation in Z
algebra
Problem Statement
Let
Z
\mathbb{Z}
Z
be the set of integers. Find all functions
f
:
Z
ā
Z
f:\mathbb{Z}\rightarrow\mathbb{Z}
f
:
Z
ā
Z
such that:
2023
f
(
f
(
x
)
)
+
2022
x
2
=
2022
f
(
x
)
+
2023
[
f
(
x
)
]
2
+
1
2023f(f(x))+2022x^2=2022f(x)+2023[f(x)]^2+1
2023
f
(
f
(
x
))
+
2022
x
2
=
2022
f
(
x
)
+
2023
[
f
(
x
)
]
2
+
1
for each integer
x
x
x
.
Back to Problems
View on AoPS