Problem Description
Given two integers A and B, find the greatest possible positive integer M, such that A % M = B % M.
Solution
This problem needs some derivation:
A%M = B%M
=> A%M - B%M = 0
=> A%M - B%M + M = M //add M on both sides
=> (A%M - B%M + M)%M = M%M //take mod on both sides
=> (A-B)%M = 0 //Since (A%M - B%M + M)%M equals (A-B)%M Modular Arithematic
So, we can say that if A%M=B%M, then A-B must be divisible by M. In other words, M is a multiple of A-B. Obviously, the largest number which can divide A-B will be the absolute of (A-B).
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public class Solution {
public int solve(int A, int B) {
return Math.abs(A-B);
}
}