MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

Functional Equation on Natural Numbers

2175ExpertAlgebraNumber Theory

Préparation Olympique Française de Mathématiques

Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $$ x f(y)+y f(x)=(x+y) f\left(x^{2}+y^{2}\right) $$ for all natural numbers $x$ and $y$. Note: recall that $\mathbb{N}$ denotes the set of natural numbers, i.e., $\mathbb{N}=\{0,1,2, \ldots\}$.
0 students attempted0% solvedRating 2175

Related practice paths

Olympiad-Style PracticeDeep contest practice for proof-style problem solving.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.