Is it permissible for me to pray alone at home instead of praying in congregation at the mosque, given the distance and the difficulty of hearing the call to prayer without a loudspeaker, which causes a waste of time and disrupts my studies?

Congregational prayer is obligatory for adult men. A mosque is not a prerequisite for it; if you pray in congregation at home, you have fulfilled your obligation. If you do not find anyone to pray with in congregation at home, then you must go to the mosque if you can hear the call to prayer without a loudspeaker under normal circumstances. If you hear it, then it is obligatory for you to come to the mosque; otherwise, you are excused from attending it. Obeying Allah and striving in worship, including congregational prayer, are among the greatest causes of happiness in this world and the hereafter, and of academic excellence.