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- Title
Two conjectures on the arithmetic in ℝ and ℂ.
- Authors
Tyszka, Apoloniusz
- Abstract
Let <BI>G</BI> be an additive subgroup of ℂ, let Wn = {xi = 1, xi + xj = xk: i, j, k ∈ {1, ..., n }}, and define En = {xi = 1, xi + xj = xk, xi · xj = xk: i, j, k ∈ {1, ..., n }}. We discuss two conjectures. (1) If a system S ⊆ En is consistent over ℝ (ℂ), then S has a real (complex) solution which consists of numbers whose absolute values belong to [0, 22n –2]. (2) If a system S ⊆ Wn is consistent over <BI>G</BI>, then S has a solution (x1, ..., xn) ∈ (<BI>G</BI> ∩ ℚ)n in which |xj| ≤ 2n –1 for each j.
- Subjects
LOGICAL prediction; ARITHMETIC functions; POLYNOMIAL operators; LINEAR statistical models; MATHEMATICAL logic; MATHEMATICAL analysis
- Publication
Mathematical Logic Quarterly, 2010, Vol 56, Issue 2, p175
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.200910004