Consequences of a Theorem of Erdös-prachar

On a Theorem of Prachar Involving Prime Powers

Let p, with or without subscripts, always denote a prime number. In this paper we are able to establish two localized results on a theorem of Prachar which states that almost all positive even integers n can be written as n = p2 + p3 + p4 + p5. As a consequence of one result, we prove additionally that each sufficiently large odd integer N can be represented as N = p1+p2+p3+p4+p5 with ∣pkk − 5 ...

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

Extremal Matroid Theory and The Erdös-Pósa Theorem

A Taste of Erdös on Interpolation

We discuss a few of Erdös’results on Lagrange interpolation, and then focus on some of the rami…cations of the Erdös-Turan Theorem on Mean Convergence of Lagrange interpolation.

Dirichlet Sets and Erdös-kunen-mauldin Theorem

By a theorem proved by Erdös, Kunen and Mauldin, for any nonempty perfect set P on the real line there exists a perfect set M of Lebesgue measure zero such that P +M = R. We prove a stronger version of this theorem in which the obtained perfect set M is a Dirichlet set. Using this result we show that the ideal of additive sets for any family generated by analytic subgroups of the reals contains...