论文部分内容阅读
K·Sastry在文[1]中定义了连贯多项式:若多项式f_n(x)与f_n(x)+1同时在数集K上可约,则称f_n(x)为K上的连贯多项式。对于二次连贯多项式,仅有一些简单结果:多项式φ(x)=x~2+bx+c与φ(x)+1=x~2+bx+c+1在整数集Z上同时可约的充要条件是b=2d,c=d~2-1,d∈Z。对于更高次的,则未见任何论述。杨之先生在[2]中考虑了一般的二次多项式y=ax~2+bx+c,提出了如下尚未解决的问题:
K.Sastry defined coherent polynomials in [1]: If the polynomials f_n(x) and f_n(x)+1 are simultaneously commensurable on the number set K, then f_n(x) is called a coherent polynomial on K. For quadratic polynomials, there are only a few simple results: polynomials φ(x)=x~2+bx+c and φ(x)+1=x~2+bx+c+1 The necessary and sufficient conditions are b=2d, c=d~2-1, d∈Z. For higher order, there is no discussion. Mr. Yang Zhi in [2] considered the general quadratic polynomial y=ax~2+bx+c and proposed the following unsolved problems: