MathDB

Function must be a bivariate polynomial

Source: Miklos Schweitzer 2023, Problem 4

March 7, 2024

polynomialanalysis

Problem Statement

Determine the pairs of sets

X,Y\subset\mathbb{R}

for which the following is true: if

f(x, y)

is a function on

X\times Y{}

such that for every

x\in X

it is equal to a polynomial in

y

on

Y

and for every

y\in Y

it is equal to a polynomial in

x

on

X

then

f

is a bivariate polynomial on

X\times Y.

Back to Problems View on AoPS