How to get the remainder of a big numbers in java

Question

is there any solution to this problem? why it returns 541 instead of 3.

public class Test {
    public static void main(String[] args) {
        double a = Math.pow(3, 561);

        // it returns 541 instead of 3
        System.out.println(a % 561);
    }
}

Answer 1

According to the Fermat's little theorem:

Math.pow(a, p) % p == a % p

and so:

Math.pow(3, 561) % 561 = 3 % 561 = 3

Therefore, you don't need to do this heavy calculations. Just maths.