Two Problems in Number Theory
Kaifu Song, Weixuan Nie · Studies in Applied Mathematics · 2013
In this paper, we will discuss two questions, the primality test for Fermat number F n and several fundamental problems in transfinite number theory. For the primality test for Fermat number Fn, this paper introduces the method of primality test for Fermat number F n and the Fermat factorization theorem. Meanwhile, the factorization theorem is used to write operation procedure, so that we can distinguish whether 2 n +2 t +1 is the divisor of F n or not. For some of the fundamental problems in transfinite number theory, this paper introduces the concept of countable expansion, and then inspects countability of the set of real numbers from the aspect of expansion. Besides, we analyze the cardinal number of linear point set, deriving the fact that their cardinal number possesses invariance.