The persian and roman empires
invaded who ?

The Roman–Persian Wars were a series of conflicts between states of the Greco-Roman world and two successive Iranian empires: the Parthian and the Sasanian. Battles between the Parthian Empire and the Roman Republic began in 66 BC; wars began under the late Republic, and continued through the Roman (later Byzantine) and Sasanian empires. Various vassal kingdoms and allied nomadic nations in the form of buffer states and proxies also played a role. The wars were ended by the Arab Muslim Conquests, which led to the fall of the Sasanian Empire and huge territorial losses for the Byzantine Empire, shortly after the end of the last war between them.

Although warfare between the Romans and Persians continued over seven centuries, the frontier, aside from shifts in the north, remained largely stable. A game of tug of war ensued: towns, fortifications, and provinces were continually sacked, captured, destroyed, and traded. Neither side had the logistical strength or manpower to maintain such lengthy campaigns far from their borders, and thus neither could advance too far without risking stretching its frontiers too thin. Both sides did make conquests beyond the border, but in time the balance was almost always restored. Although initially different in military tactics, the armies of both sides gradually adopted from each other and by the second half of the 6th century they were similar and evenly matched.[1]

The expense of resources during the Roman–Persian Wars ultimately proved catastrophic for both empires. The prolonged and escalating warfare of the 6th and 7th centuries left them exhausted and vulnerable in the face of the sudden emergence and expansion of the Caliphate, whose forces invaded both empires only a few years after the end of the last Roman–Persian war. Benefiting from their weakened condition, the Arab Muslim armies swiftly conquered the entire Sasanian Empire, and deprived the Eastern Roman Empire of its territories in the Levant, the Caucasus, Egypt, and the rest of North Africa. Over the following centuries, more of the Eastern Roman Empire came under Muslim rule.

https://en.wikipedia.org/wiki/Roman%E2%80%93Persian_Wars

where are the statements?