In the study of papyri and ancient history Egypt is usually referred to as Graeco-Roman Egypt for the period going from the third century BC to approximately the third century AD, during which time the country was first under the Ptolemies (III-I BC) and then under the Romans (AD I-III). The phrase Graeco-Roman Egypt, the significance of which has been long debated, simply points to the existence of a multi-cultural society where Egyptian, Greek and, later on, Roman customs and traditions met and intermingled. Various elements of Greek culture found their way into Egypt with the arrival of the Ptolemies; some kept their original form and nature, some others underwent a more or less deep transformation and acquired a somehow hybrid connotation. Religion was of course one of these elements (see post http://blogs.lib.berkeley.edu/tebtunis-papyri.php/what-is-greek-in-tebtunis), but not the only one.
The most representative element to mark the encounter between the Greeks and the Egyptians is certainly the language. Greek penetrated into Egypt in the third century BC as the language of the rulers, and for a time was used only by Greek settlers. But this state of things was bound to change soon. With Egypt quickly becoming a multi-cultural society, Greek became increasingly more popular. And not only among the Hellenic strata of the population. Greek also started to be used by many Egyptians in private correspondence and business documents, a phenomenon that seems to have increased in the Roman period. Under the Ptolemies both demotic-Egyptian and Greek were adopted in the administration, but around 146 BC a royal decree was imposed whereby Egyptian contracts (that is contracts written in demotic) required Greek subscriptions in order to be valid. This seeminlgy simple requirement was the beginning of a big social and cultural change in the life of the Egyptians. Towards the end of the first century AD, as a result of a Roman policy, demotic completely disappeared from administration and legal documents, making Greek the official language of Egypt.
Here are two examples of demotic documents dated to the Ptolemaic period (II BC) with Greek subscriptions, from the Tebtunis collection at CTP.
P.Tebt. III 982 P.Tebt. II 571