I have an application that needs to display number of followers and following (users/show.json
) for a random user on a public page (authentication is not requir
Yes, it is possible! If your application doesn't need to do things like post statuses or send direct messages on behalf of a user, you should be able to retrieve all of a user's public information with a single hardcoded set of Twitter OAuth credentials, and not require the user to authenticate.
If you're not comfortable using the Twitter API directly, there are a number of good API wrappers out there for various languages -- among others, the Temboo SDK, which will give you code snippets for calling various methods (and also gives you a place to securely store your Twitter credentials, so you don't need to bake them into your application).
Take a look at:
(Full disclosure: I work at Temboo.)
The easiest way to do what you're asking is to use Twitter API 1.1's 'application-only authentication' feature, which works for much of the API. See Application-only authentication. You can see a Python example of it in get_bearer_token.py.
Once you have a bearer token, you only need to include that in your request authorization header - signing is not necessary.