Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2023 OIM Problems/Problem 2

Revision as of 02:13, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>\mathbb{Z}</math> be the set of integers. Find all functions <math>f: \mathbb{Z} \to \mathbb{Z}</math> such that: <cmath>2023f(f(x))+2022x^2=2022f(x)+...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $\mathbb{Z}$ be the set of integers. Find all functions $f: \mathbb{Z} \to \mathbb{Z}$ such that:

\[2023f(f(x))+2022x^2=2022f(x)+2023[f(x)]^2+1\]

for each integer $x$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://sites.google.com/associacaodaobm.org/oim-brasil-2023/pruebas

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_OIM_Problems/Problem_2&oldid=207192"