Question

Find the no of positive integral solutions for the equations (1/x) + (1/y) = 1/N! (read 1 by n factorial) Print a single integer which is the no of positive integral solutions modulo 1000007.

Input:
N
Output:
Number of positive integral solutions for (x,y) modulo 1000007
Constraints:
1 <= N <= 10^6
Sample Input00:
1
Sample Output00:
1


Sample Input01:
32327
Sample Output 01:
656502

Sample Input02:
40921
Sample Output 02:
686720

Answer 1

Sample Problem Statement:

Given an integer N, print 'hello world' N times.

Sample Input
5
Sample Output
hello world
hello world
hello world
hello world
hello world

Solution in C
_________________
#include <stdio.h>
int main() {
int i, n;
scanf("%d", &n);
for (i=0; i<n; i++) {
printf("hello world\n");
}
return 0;
}

Answer 2

Anyone?

Answer 3

http://sharathpan.wordpress.com/2012/05/17/interview-street-equations-solution/

Answer 4

No of solutions for the equation XY=N! is
(e1+1)(e2+1)………..(en+1)
where e1,e2…en are multiplicities of Prime Numbers below N.

For Ex: XY=4!
No of primes below 4= {2,3}
4!= 24= 23*31
where 3 and 1 are prime multiplicities of 24.
so applying the formula (3+1)*(1+1)=8 (no of factors of 24={1,2,3,4,6,8,12,24}.

Now the equation 1⁄x+1⁄y= N! can be transformed into
(x-N!)(y-N!)=N!2
Hence No. of solutions of the above equation is
(2e1+1)(2e2+1)………..(2en+1)

Hence to solve the problem:
1) First find out the primes less than N
2) Find the prime multiplicities
3) Apply the formula.

Answer 5

thanks @mayankdevnani

Answer 6

welcome