Final answer:
The Abbasid Caliphate was primarily concerned with religious conflicts, border disputes, economic competition, and the drive for territorial expansion in their dealings with the Byzantine Empire. The translation movement exemplified their efforts to match Byzantine cultural prestige. The correct option is A.
Step-by-step explanation:
The Abbasid Caliphate had several concerns when dealing with the Byzantine Empire. One of the primary concerns was religious conflicts and border disputes, as their territories edged against one another, leading to significant tensions.
Another concern was the economic competition and the pressure for territorial expansion. The cultural and administrative influence of the Byzantines was recognized by the Abbasids, who undertook the translation movement to absorb Greek knowledge into the Arabic language to bolster their own cultural and intellectual standing.
Additionally, internal divisions and the challenge of managing a vast empire contributed to the weakening of the Abbasid Caliphate, making diplomatic interactions with the Byzantine Empire more complex. The correct option is A.