Difference between for long time, for a long time?

Hi,
I Would like to know what is the difference between for long time and for a long time?

Thank you!

for long time is incorrect English (but a common mistake by foreign speakers)
for a long time is correct English.

If it was spoken, it's possible that the speaker spoke very quickly, making the 'a' difficult to hear.

Hope that helps.
:)
Martin