Utilizing the Properties of Residue Class Ring to Solve Several Probability Problems in Determinant
Liang Ying · Journal of Anqing Teachers College · 2011
Let M be a n-determinant whose entries take the numbers from the set-{kr+i∶k∈Z},(i=0,1,2,…,r-1) with the equal probability,where r is larger than 1,and randomly takes a positive number.Making the value of that determinant to divide r,the remainder will take the elements from the set-{0,1,2,…,r-1}according to a certain law.This paper,on the basis of the related theories of Residue Class Ring from Abstract Algebra,makes an effort to initiate the instrumental research pointing to this problem and,consequently,achieves several conclusions.