Some representations of unlimited natural numbers

Bellaouar Djamel; Boudaoud Abdelmadjid

Vol. 28 No. 2 (2023)

Regular Articles

Some representations of unlimited natural numbers

Published 2023-10-19

Bellaouar Djamel
Boudaoud Abdelmadjid

Bellaouar Djamel
University 08 Mai 1945 Guelma

Boudaoud Abdelmadjid
University of M'sila

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Abstract

Based on the work of K. Hrbacek [12], we prove that every unlimited natural number ω is of the form ω=ω₁⋅ω₂+ω₃⋅ω₄ in at least k different ways (k≥1 is limited), where ω_{i}∈N is unlimited and ω_{i}/ω_{j} is appreciable for 1≤i,j≤4. Other similar representations of unlimited natural numbers are also presented.

Keywords

factoring of integers, nonstandard analysis, unlimited integers.

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