p^k元域F的单超越扩域E上的方程y^n=D与Ay^(2n)+By^n+C=0

THE EQUATIONS y^n=D AND Ay^(2n)+By^n+C=0 OVER A SIMPLE TRANSCENDENTAL EXTENSION FIELD E OF A FIELD F OF p^k ELEMENTS

设F是 pk 元域 ,E是F的单超越扩域 ,给出E上的方程 yn=D与Ay2n+Byn+C =0 (A≠ 0 )在E中有根或没有根的条件 .若方程有根 ,则同时给出根的个数 .

Let F be a field of p k elements and E be a simple transcendental extension field of F.In this paper,the author gives the conditions that the equations y n=D and Ay 2n +By n+C=0 (A≠0) over the E have roots or have no roots in the E.If the equations have roots,then the author gives the number of the roots at the same time.