The concrete theory of numbers: initial numbers and wonderful properties of numbers repunit

Abstract

In this work initial numbers and repunit numbers have been studied. All numbers have been considered in a decimal notation. The problem of simplicity of initial numbers has been studied. Interesting properties of numbers repunit are proved: $gcd(R_a,R_b)=R_{gcd(a,b)}$; $R_{ab}/(R_a{R}_b)$ is an integer only if $gcd(a,b)=1$, where $a\ge 1$, $b\ge 1$ are integers. Dividers of numbers repunit, are researched by a degree of prime number.

8 pages ; v3: minor grammatical changes, etc