Structure of the Multiplication Table for [ modulo P ]

Section I : Introduction

This paper is an attempt to set up a frame-work for the { multiplicative field } for [ modulo P ] , with [ P ] being a { prime number } .

The general flow of the paper is as follows :

The 'Square-Of-Square' { Pyramids } & { RING's } are re-vitalized , with this concept here dating back to :
- { An Approach to the Characteristics of Numbers } , first published in November , 2003 .
We then looked at the { multiplicative fields } for the 3 { prime numbers } :
- [ 233 ] = 8 x 29 + 1 ,
- [ 1103 ] = 2 x 19 x 29 + 1 ,
- [ 3361 ] = 32 x 3 x 5 x 7 + 1 ;
  
  each having a higher level of complications .
We then looked at { FIRON - 2/P } , being defined by the smallest non-zero value of [ N ] satisfying the equation :
And { FIRON - 2/P } is controlling on the 'Square-Of-Square' { RING's } and the { multiplicative conjugates } [ modulo P ] .
Finally , we looked at the original { Chinese Remainder Theorem } , back from circa { 0 - 500 A.D. } ,
- and we were able to find an application here for the { multiplicative conjugates } [ modulo P ] .

This , hopefully , will build a stronger foundation for a better understanding of { prime numbers } ,

and let us look more closely at :
- the { Divisibility of a [ binary-code number ] by an [ 'odd' prime number ] } ,
  
  a subject being explored in my other paper :
  - ( The { Odd-On-Odd Format } for { Odd Numbers } ) , dated 2006-4-11 & 2006-5-05 .