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太失败了,这么简单的题居然交了13次才通过。个人思路:
设输入的是abcd,假设其解是n进制,则有
(a*n*n*n + b*n*n + c*n + d)%(n-1)=0
则有:( (a*n*n*n)%(n-1)+
(b*n*n)%(n-1)+
(c*n)%(n-1)+
d )%(n-1)=0
则有:( (a* (n%(n-1)) *(n%(n-1)) *(n%(n-1)))+
(b* (n%(n-1)) *(n%(n-1)))+
(c* (n%(n-1) +
d ) %(n-1)=0
则有: (a*1*1*1+b*1*1+c*1+d)%(n-1)=0
则有:(a+b+c+d)%(n-1)=0
所以,经过转换,变为求输入数的各数位的和能%(n-1)等于0;
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