With whose definition of knowledge does edmund gettier, the philosopher who challenged the tripartite definition of sentential knowledge, find to successfully state the necessary and sufficient conditions for someone's knowing a given proposition?

The sufficient conditions are given by Plato with definition of knowledge does Edmund Gettier.

Edmund Gettier published a 3-page paper which challenged the definition of knowledge which has been defined and accepted since Plato. According to Plato, to have knowledge of something the following conditions must be met: justification, truth and belief.  

This means that “justified true belief” also referred to as JTB defines knowledge of a claim. Gettier’s paper challenged this definition by presenting two examples which disproved the long-accepted definition of knowledge. One example showed that there are cases where one can have a justified true belief about something or claim without actually having knowledge of the same claim.