Lets wait for 2016

Computer Science Level 4

1 2014 + 2 2014 + 3 2014 + . . . + 201 4 2014 ( m o d 2016 ) \large 1^{2014}+2^{2014}+3^{2014}+...+2014^{2014} \pmod{2016}


The answer is 335.

Mehul Chaturvedi by Mehul Chaturvedi , 22, India

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4 solutions

Brock Brown
Feb 27, 2015

Python: 

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total = 0
for n in xrange(1,2015):
    total += n**2014
print "Answer:", total % 2016

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Alex Li
Mar 9, 2015 
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public class x
{
    public static int power2014(int x)
    {
        int z = 1;
        for(int i = 0; i<2014; i++)
        {
            z = (z*x)%2016;
        }
        return z;
    }
    public static void main(String[] args) throws IOException
    {
        int total = 0;
        for(int i = 1; i<2015; i++)
        {
            total += power2014(i);
        }
        System.out.println(total%2016);
    }
}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Kunal Verma
May 7, 2016

C++: 

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#include <iostream>
using namespace std;
int modexp(int a, int b, int n)
{
    int prod=1;
    for(int i=1;i<=b;i++)
    {
        prod*=a;
        prod=prod%n;
    }
    return prod;
}
int main()
{
    long sum=0;
    for(int i=1;i<=2014;i++)
        sum+=modexp(i,2014,2016);
    cout << sum%2016;
    return 0;
}

Answer computes in 0.078s.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nguyen Thanh Long
Jan 20, 2015

int find remainder 5() { int iK = 0, tmp = 1; List<int> ar = new List<int>(); for (int i = 1; i <= 2014; i++) { tmp = i; for (int j = 1; j < 2014; j++) { tmp = (tmp * i) % 2016; } iK = (iK + tmp) % 2016; } return iK; }

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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