Here is the official info from the Turkish ministry of Foreign Affairs:
Egypt: Official passport holders are exempted from visa for their travels up to 90 days.
Ordinary passport holders are required to have visa to enter Turkey. Ordinary passport holders may obtain their 30-day single-entry e-Visas via www.evisa.gov.tr, provided that they have a valid Schengen or OECD visa or residence permit and that they travel to Turkey with Turkish Airlines or Egypt Air.
Besides, those ordinary passport holders who are under 20 or over 45 years old may get their 30-day single-entry e-Visas via the website www.evisa.gov.tr.
Since having a visa is required to enter the country, you most likely won't be able to meet your friends without one.
On the other hand, “Schengen or OECD visa or residence permit” sounds very broad (i.e. not limited to Schengen type C visa but could also cover a type D visa like yours, which is essentially a form of residence permit) so if you are travelling with Turkish Airlines or Egypt Air, you might be able to get an e-visa easily. I am not familiar with Turkish law and I am not sure if Turkish authorities do accept German student visas for this in practice but it seems worth a try.