Mentioning a Professor and his comment in a mail without his permission
You should ask permission from Prof. X.

Quoting a statement like "the analytical results are correct" implies endorsement to some degree. 

You should be very careful not to say anything that could imply endorsement without permission of the "endorser." 

Note that if he does give permission, you still have to be careful not to quote his statement out of context. For example, you should not say 


  Prof. X said my analytical results are correct.


instead, you should explain what he really said, more like


  I showed this work to Prof. X. He said that the analytical results seem correct, but not practical, and he suggested that I look into approximation algorithms.