Find perfect squares whose difference is a repunit; see https://math.stackexchange.com/questions/3674784.

Question3674784.java

import java.math.BigInteger;

public class Question3674784 {
    public static void main(String [] args) {
        for (int n = 1;;n++) {
            System.out.println(n);
            BigInteger diff = BigInteger.TEN.pow(n).subtract(BigInteger.ONE).divide(BigInteger.TEN.subtract(BigInteger.ONE));
            BigInteger x = BigInteger.TWO;
            BigInteger x2 = x.multiply(x);
            BigInteger y = BigInteger.ONE;
            BigInteger y2 = y.multiply(y);
            do {
                while (x2.subtract(y2).compareTo(diff) < 0) {
                    x = x.add(BigInteger.ONE);
                    x2 = x.multiply(x);
                }
                if (x2.subtract(y2).equals(diff)) {
                    System.out.println(x + "^2 - " + y + "^2 = " + x2 + " - " + y2 + " = " + diff);
                    x = x.add(BigInteger.ONE);
                    x2 = x.multiply(x);
                }
                while (x2.subtract(y2).compareTo(diff) > 0) {
                    y = y.add(BigInteger.ONE);
                    y2 = y.multiply(y);
                }
            } while (!x.equals(y));
        }
    }
}