用二项式定理解答 99的100次方减1被100整除

99^100-1
=(100-1)^100-1
=100^100-C(100,1)*100^99+C(100,2)*100^98-...+C(100,98)*100^2-C(100,99)*100+1-1
=100*[100^99-C(100,1)*100^98+C(100,2)*100^97-...+C(100,98)*100-C(100,99)]

(99^100-1)/100
=((100-1)^100-1)/100
=(100^100-C(100,1)*100^99+C(100,2)*100^98-...+C(100,98)*100^2-C(100,99)*100+1-1)/100
={100*[100^99-C(100,1)*100^98+C(100,2)*100^97-...+C(100,98)*100-C(100,99)]}/100
=100^99-C(100,1)*100^98+C(100,2)*100^97-...+C(100,98)*100-C(100,99)