对于费马小定理，
ap−1≡1(mod p)a^{p-1}\equiv 1(\mod p )ap−1≡1(modp)
若 ppp 不为质数，是否存在
p=p1e1×p2e2×…⋯×pkekp=p_1^{e_1}\times p_2^{e_2}\times \dots \dots \times p_k^{e_k}p=p1e1×p2e2×…⋯×pkek alcm(e1−1,e2−1,e3−1,……,ek−1)≡1(mod p)a^{lcm(e_1-1,e_2-1,e_3-1,\dots\dots,e_k-1)}\equiv1(\mod p)alcm(e1−1,e2−1,e3−1,……,ek−1)≡1(modp)
p=p1e1×p2e2×…⋯×pkekp=p_1^{e_1}\times p_2^{e_2}\times \dots \dots \times p_k^{e_k}p=p1e1×p2e2×…⋯×pkek
alcm(e1−1,e2−1,e3−1,……,ek−1)≡1(mod p)a^{lcm(e_1-1,e_2-1,e_3-1,\dots\dots,e_k-1)}\equiv1(\mod p)alcm(e1−1,e2−1,e3−1,……,ek−1)≡1(modp)
蒟蒻在线求助
