多项式f(x)mod p不可约的一种判别算法

An Algorithm for the Determination of the Unreducibility of Polynomial f(x)mod p

利用有限域上推广的Euler Fermat定理对f(x)modp的可约性进行研究 ,给出了一种判别多项式f(x)modp不可约算法 .该算法通过随机选取F上满足αm(x)≡ 1 (modf(x) )的多项式α(x) ,以及m的因子k ,并由 (am/q(x) - 1 ,f(x) ) =1 (q是k的任一素因子 ) ,来确定f(x)modp的不可约性 .

According to popularized Euler Fermat theorem in finite field adopted to research the reducibility of f(x) mod p, an algorithm is presented to determine this polynomial that is not reducible, by means of selecting randomly polynomials α(x) that conform to α m(x)≡1(mod f(x))and factors k of m, then using ( α m/q (x) 1,f(x))=1(q is any factor of k)for the final determination.