【摘要】 文献[3]中给出了同余式x^M≡1（modn）的解数公式,文献[1]中给出了二项同余式x^m≡a（modn）有解的判别条件。本文先证明x^m≡a（modn）有解时,其解数与a无关,从而x^M≡1（modn）的解数公式也是有解同余式x^m≡a（modn）的解数公式。同时给出了一个直接求X^m≡1（modn）的所有解的方法和一个由x^m≡a（modn）的某一解求其所有解的方法。最后给出了一个联系任意a对modn的次数Y_?（n）的有趣的公式。更多还原

【Abstract】 We have given the formula of number of solutions of the comgruence xm≡a(modn) in[3] ,the criterion for the comgruence xm=a(modn) have solutions,in[1]. This article prived-. If xm -a(modn) have solutions, then the number of its solutions is not relative to a, hence the formula of the number of solutions of the comgruence x"=l(modn) is the formula of the number of solutinos of the comgruence xm≡a(modn) ,too. Moreover, this article gave an immediate method to solve the all solutions of the comgruence xm≡(modn) and a method to’ solve the all solutions for the comgruence xm≡a(modn), when known its a solution. Lastly this article gave a interesting formula being relative to Y (n) ,any a’s order to modn.更多还原