Count the number of solutions to a=-d, a^2+bc=1 mod 26; see http://math.stackexchange.com/questions/324542.

Question324542.java

import java.util.Set;
import java.util.HashSet;

public class Question324542 {
    final static int n = 26;

    public static void main (String [] args) {
        Set<Integer> residues = new HashSet<Integer> ();
        for (int i = 0;i < n;i++)
            residues.add ((i * i) % n);

        int count = 0;

        for (int b = 0;b < n;b++)
            for (int c = 0;c < n;c++) {
                int r = (1 - b * c + 26 * 26) % 26;
                if (residues.contains (r))
                    count += r == 0 || r == 13 ? 1 : 2;
            }

        System.out.println (count);
    }
}