I'm learning modular exponentiation with Chinese remainder theorem.


I found a great answer from below
[http://crypto.stackexchange.com/questions/5296/how-can-i-use-eulers-totient-and-the-chinese-remainder-theorem-for-modular-expon][1]

But I can't understand the last step of construction from Cp and Cq very well. Can someone explain it to me? Moreover, if I make N = 55 = 11 x 5 instead of 5 x 11, that last step fails to give correct answer. 

The last step:
M^e mod pq=Cq+q⋅((Cp−Cq)mod p)

 


  [1]: http://crypto.stackexchange.com/questions/5296/how-can-i-use-eulers-totient-and-the-chinese-remainder-theorem-for-modular-expon