MathDB
Miklós Schweitzer 2007 Problem 7

Source:

March 3, 2017
Miklos Schweitzerreal analysis

Problem Statement

Prove that there exist natural numbers nk,mk,k=0,1,2,…n_k, m_k, k=0,1,2,\ldots, such that the numbers nk+mk,k=1,2,…n_k+m_k, k=1,2,\ldots are pairwise distinct primes and the set of linear combination of the polynomials xnkymkx^{n_k}y^{m_k} is dense in C([0,1]×[0,1])C([0,1] \times [0,1]) under the supremum norm.
(translated by Miklós Maróti)
Back to ProblemsView on AoPS