Lightoj 1236 - Pairs Forming LCM
The problem statement actually refers to finding out number of pairs of integers that have LCM n ( which is the given value). There can be 2000 test cases and value of n can be at most 10 14 . let's assume that the prime factorization of n can be represented as n = p1 q1 .p2 q2 .......px qx , where p1,p2....px are prime numbers and q1,q2...qx are corresponding powers. lets assume that any two integers are i and j such that LCM(i,j)=n. since n is their LCM, the prime factorization of i and j must have the following qualities. 1. if i = px qx then j must be either j = px qx-1 or j = px qx-2 or ..... j = px 0 2. if j = px qx then i must be either i = px qx-1 or i = px qx-2 or ..... i = px 0 3. i = px qx and j = px qx for the 1st scenario we can see there are qx combinations for the 2nd scenario we can see there are qx combinations for the 3rd scenario we can see there are 1 combinations so, there can be a total of 2*qx + 1 combinations for each of the pr...