The Origins of Early Christianity.

http://www.livius.org/di-dn/diaspora/diaspora.htm

A second impulse for the Jews to go abroad was the foundation of Alexandria in Egypt by Alexander the Great (331 BCE). Under the next Egyptian kings, the Ptolemies, Jewish mercenaries and merchants settled in the capital of the country along the Nile. Several other communities in the Ptolemaean empire are known: e.g., at Pelusium, Leontopolis, and Cyrene. According to Philo, a Jewish author from the early first century CE, about a million Jews were living in Egypt.

They spoke Greek; therefore, the Bible was translated (the so-called Septuagint). In many diasporic communities, this text was to become more authoritative than the Hebrew text.

http://www.livius.org/di-dn/diaspora/rome.html

Synagogue of the Hebrews and Vernacular synagogue: the name of the first one suggests that it was the first synagogue in Rome, or that it maintained the Hebrew liturgical language; the second name suggest that Latin was spoken.