1. Prove the following: a.a=b (mod n ) implies b =a (mod n) b. a=b (mod n) and b=c (mod n) imply a=c (mod n) 2. Prove the following: a. [( a mod n ) - ( b mod n )] mod n = ( a - b ) mod n b. [( a mod...

1. Prove the following:

a.a=b (mod n ) implies b =a (mod n)

b. a=b (mod n) and b=c (mod n) imply a=c (mod n)

2. Prove the following:

a. [(amodn) - (bmodn)] modn= (a-b) modn

b. [(amodn) x (bmodn)] modn= (axb) modn