Is it possible to have a client app which can authenticate using Facebook but without requiring browser(I mean no embedded browser in the code)?? User inputs the username/passwo
absolutely yes, but, we'll need to know which programming language you want to use before we can give much advice.
For example, it's possible using httpclient for java and python to encapsulate all the functionality you need, others can chime in with libraries that they use for C, C++, perl, etc.
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search for httpclient and how it's used with python. if you run wireshark on your system, you will be able to watch the data interchange (if you don't understand the http protocol completely) and then implement that in your code.
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