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Two conjectures on the arithmetic in ℝ and ℂ

✍ Scribed by Apoloniusz Tyszka

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
163 KB
Volume
56
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

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, 2 2 n-2

].

(2) If a system S ⊆ Wn is consistent over G, then S has a solution (x1, . . . , xn) ∈ (G ∩ Q) n in which |xj| ≤ 2 n-1 for each j.

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