@MISC{INT_7.MIZ,
  AUTHOR = {Okazaki, Hiroyuki and Shidama, Yasunari},
  TITLE = {Uniqueness of factoring
    an integer and multiplicative group $Z/pZ^{*}$},
  SECTION1 = {Uniqueness of factoring an integer},
  SECTION2 = {multiplicative group $Z/pZ^{*}$},
  DAY = {31},
  MONTH = {January},
  YEAR = {2008},
  ADDRESS1 = {Shinshu University, Nagano, JAPAN},
  ADDRESS2 = {Shinshu University, Nagano, JAPAN},
  SUMMARY = {In the MML article \cite{INT_3.ABS}, it had proven
  that the Integers modulo $p$, in this article we shall refer as
  $Z/pZ$, constitutes a field if and only if $p$ is a prime.
  Then the prime modulo $Z/pZ$ is an additive cyclic group and
  $Z/pZ^{*}=Z/pZ\setminus\{0\}$ is a multiplicative cyclic group, too.
  The former has been proven in the MML article
  \cite{GR_CY_1.ABS}.
  However, the latter had not been proven yet.
  In this article, first, we prove a theorem concerning the LCM
  to prove the existence of primitive elements of $Z/p^{*}$.
  Moreover we prove the uniqueness of factoring  an integer.
  Next we defined the multiplicative group $Z/pZ^{*}$ and prove
  it is cyclic.}}

