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  • Ignatius's puzzle

    Ignatius's puzzle

    Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
    Total Submission(s): 4935    Accepted Submission(s): 3359


    Problem Description

    Ignatius is poor at math,he falls across a puzzle problem,so he has no choice but to appeal to Eddy. this problem describes that:f(x)=5*x^13+13*x^5+k*a*x,input a nonegative integer k(k<10000),to find the minimal nonegative integer a,make the arbitrary integer x ,65|f(x)if
    no exists that a,then print "no".

     

     

    Input

    The input contains several test cases. Each test case consists of a nonegative integer k, More details in the Sample Input.

     

     

    Output

    The output contains a string "no",if you can't find a,or you should output a line contains the a.More details in the Sample Output.

     

     

    Sample Input

    11 100 9999

     

     

    Sample Output

    22 no 43

     

     

    Author

    eddy

     

    若对任意x成立,则当x=1时必然成立.若当x=1时成立,则对任意正整数x都成立.

    观察题目中给出的式子可以看出每一项都有公因子x,所以f(x)必然是f(1)的x倍,若f(1)是65的倍数,则f(x)必然也是65的倍数.

    #include<stdio.h>
    int main()
    {
        int k;
        while (scanf("%d",&k)!=EOF)
        {
            if (k==1 || (k%5!=0 && k%13!=0 && k%65!=0))
            {
                for (int i=1;;i++)
                if ((18+k*i)%65==0)
                {
                    printf("%d
    ",i);
                    break;
                }
            }
            else printf("no
    ");
        }
        return 0;
    }

     

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  • 原文地址:https://www.cnblogs.com/dramstadt/p/3188831.html
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