how to use wordpress authentication for user login in my android app

Solution:

Well, what I´ll do is this:

1. Create a plugin in WP that give you a REST Webservice and by access to your WP database you always knew when a user is login, logout, last access and get all the info you want or make any action on your WP site.
2. Then when you have the Webservices you can use it in your android app or other application. Here you have a full example how to call a REST Webservices in Android (http://developer.xamarin.com/recipes/android/web_services/consuming_services/call_a_rest_web_service/)

Here a HTTP REST API plugin for wordpress (https://wordpress.org/plugins/json-rest-api/). And here the authentication guide (http://wp-api.org/guides/authentication.html)

Hope that can help you .