对初等数论中解X^n≡a(modm)的探讨

The Approach of the Solving Congruences x^n≡a (modm)in Elementary Number Theory

对于解同余式x^n≡a(modm)(1)中只给了以m=2,4,p^a,2p^a为模时的有解条件,本文研究了当m=2~a,a>2时x_n≡a(mod2~a)的解法。并给出了对任意m>1时,x^n≡a(modm)的有解条件,解法和解的个数。

About solving congruences x^n≡a(modm), only gave the condition of having solution as m = 2, 4, p^a,2p^a.In this paper prove the solving method of x^n≡(mod2~a)α>2, and give the having solution condition, solving method and solutions number of x^n≡(modm),m>1。