This is a cryptology question from the textbook Introduction to Modern Cryptography by Katz and Lindell.

8.9 Let p, N be integers with p|N. Prove that for any integer X, mod N) mod p1-IX mod p]. Show that, in contrast, [[X mod p] mod N] need not equal [X mod 8.9 Let p, N be integers with p|N. Prove that for any integer X, mod N) mod p1-IX mod p]. Show that, in contrast, [[X mod p] mod N] need not equal [X mod