10.3969/j.issn.1001-4616.2015.04.006
丢番图方程ax+by=n的一个注记
令a,b为互素的正整数,n为非负整数.D(a,b;n)表示不定方程ax+by=n的非负整数解(x,y)的个数.Tripathi证明了D(a,b;n)=n/ab +1/2(1/a+1/b)+ 1/aa-1∑j=1 ζ-jna/1-ζbia+1/bb-1∑k-1ζ-knb/1-ζakb,其中ζm=e2mi/m.在本文中,我们建立了D(a,b;n)的递推关系,从而给出了上述结论的新证明.
丢番图方程、生成函数、留数定理
38
O15;O24
Project of Graduate Education Innovation of Jiangsu ProvinceKYLX_0690;Research Fund for the Doctoral Program of Higher Education of China20133207110012;the Doctoral Starting up Foundation of Qufu Normal University
2016-03-22(万方平台首次上网日期,不代表论文的发表时间)
共4页
32-35