关于数F(a)的存在性,有关性质及求法

On the Existense of the Number F(a) ,its Properties and Algorithm

本文证明了对任意的正整数a若a与10互质,即(a,10)=1,则存在最小的正整数F(a),使得有一个全部由数字1组成的F(a)位数G(a)=11……1能被a整除,即a|G(a),进一步还讨论了数F(a)的有关性质及确定F(a)的方法,这些方法是可以在计算机上实现的。

In this paper we have reached the following conclusion. For each positive integer a the rlatively prime integer 10,there exists a positive integer G(a) = 11 … 1 composed of 1's with the least number F(a)of digits so that a can divide G(a). Several properties of the number F(a) are also discussed. An algorithm for finding F(a) that can be carried out by using a computer is given.