关于多项式唯一性问题

Questions on the Unique of Polynomials

推广了Adam s-Straus关于多项式唯一性的一个定理,得到结果:设p与q皆为非常数的多项式,a1,a2,…,ak及b为k+1个互异有穷复数,若ki=1(p-ai)=0 ki=1(q-ai)=0,p-b=0 q-b=0,并且有d k≠0,i=1(z-ai)dzz=b≠0,则p≡q。

In this paper,a result by Adams-Straus on the unique of polynomials is generalized, by proving the following theorem ： Let p and q are two nonconstant Polynomials, a1, a2,…, ak and b are k＋1 distinct points in C, Satisfy： ↑k∏↓i=1（p-ai）=0〈=〉q-b=0, p-b=0〈=〉q-b=0, and d[↑k∏↓i（z-ai）]/dx｜x=b≠0, then p≡q.