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On the Erdős-Turán additive base conjecture

Theophilus Agama

Abstract

In this paper, we formulate and prove several variants of the Erdős-Turán additive bases conjecture.

On the Erdős-Turán additive base conjecture

Abstract

In this paper, we formulate and prove several variants of the Erdős-Turán additive bases conjecture.

Paper Structure

This paper contains 7 sections, 9 theorems, 48 equations.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. The Circle of Partition
  4. The Density of Points on the Circle of Partition
  5. Ascending, Descending and Stationary Circles of Partition
  6. The $l^{th}$ Fold Energy of Circles of Partition
  7. Remarks

Key Result

Proposition 3.4

Each axis is uniquely determined by points $[x]\in \mathcal{C}(n,\mathbb{M})$.

Theorems & Definitions (30)

  • Conjecture 2.1: Erdős-Turán
  • Conjecture 2.2: Erdős-Turán
  • Definition 3.1
  • Definition 3.2
  • Remark 3.3
  • Proposition 3.4
  • proof
  • Corollary 3.5
  • proof
  • Definition 4.1
  • ...and 20 more