Super number roots and factorizations for a kind of polynomial
摘要
It is widely known that the equation x2 = x has and only has two roots 0 and t. Jiglevich A. B. and Petrov N. N.discovered that equation has two other roots, i.e. infinite place's numbers (called super numbers): X 821 2890625 and Y = 1787109376, and obtained 4 (super number) roots of the equation x2 =x. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial P(x)=∏n i=l(x-ai), ai ∈ Z,i = 1,2,...,n has and only has different n2 super number roots; 2) When n＞2 and n ≠6, those n2 roots of the polynomial P(x) can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In Z* ring of super number, the polynomial P(x)=∏n i=l(x-ai),ai ∈ Z, i = 1,2,..., n has n! different factorizations.