problem66.bean

// -*- Java -*- (Just makes things look nicer)

import java.math.BigInteger;

dio(s) {
  a0 = Math.floor(Math.sqrt(s));
  if (a0 * a0 == s)
    return BigInteger.ZERO;

  s = BigInteger.valueOf((long)s);

  m = BigInteger.ZERO;
  d = BigInteger.ONE;
  a = BigInteger.valueOf((long)a0);

  n1 = BigInteger.ONE;
  n0 = a;

  d1 = BigInteger.ZERO;
  d0 = BigInteger.ONE;

  while (true) {
    if (n0.multiply(n0).subtract( s.multiply(d0).multiply(d0) ).equals(BigInteger.ONE))
      return n0;

    m = d.multiply(a).subtract(m);
    d = s.subtract( m.multiply(m) ).divide(d);
    a = BigInteger.valueOf((long)a0).add(m).divide(d);

    n2 = n1;
    n1 = n0;
    d2 = d1;
    d1 = d0;

    n0 = a.multiply(n1).add(n2);
    d0 = a.multiply(d1).add(d2);

  }
}

maxd = null;
maxx = BigInteger.ZERO;
for (i = 1; i <= 1000; i++) {
  x = dio(i);
  if (x.compareTo(maxx) > 0) {
    maxx = x;
    maxd = i;
  }
}
print(maxd);