Find all single elements in an array
I think this is the sort of thing for which HashSet is perfect. Your implementation would look something like I have shown below. The advantage is that you don't need a sort so your running time is strictly linear.

(Updated to fix syntax errors)

public static Integer[] outputSinglePair(Integer[] numbers){  
    if(numbers == null)
        throw new IllegalArgumentException();

    HashSet&lt;Integer&gt; result = new HashSet&lt;Integer&gt;();
    for (int next: numbers) {
        if (result.contains(next)) {
            result.remove(next);
        }
        else {
            result.add(next);
        }
    }
    return result.toArray(new Integer[result.size()]);
}