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7

Part of 2007 Miklós Schweitzer

Problems(1)

Miklós Schweitzer 2007 Problem 7

Source:

3/3/2017
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)
Miklos Schweitzerreal analysis