有限域上方程的解

The solutions of equations over a finite filed

讨论有限素域Fp上方程在其扩域Fq(q=pk,k≥2)上的解的情形,得出Fp上2次方程在Fp2上皆有2个解,Fp上3次、4次、6次方程在Fp3、Fp4、Fp6上皆有解.

It was discussed that the characters of the solutions of the equations over a finite prime filed F_p on its finite extension field F_q(q=p^k,k≥2),and had given that the quadratic equations with 1 variable over F_p has 2 solutions on F_(p^2),the culic equations,the quartic equtions and the hexagonal equations with 1 variable over F_p has a solution F_(p^3),F_(p^4),F_(p^6) respectively.