In Section 2.3, we define the congruence relationship as

Authors:

William Stallings

Chapter:

Introduction To Number Theory

Exercise:

Problems

Question:6 | ISBN:9781292158587 | Edition: 7

Question

In Section 2.3, we define the congruence relationship as follows: Two integers a and b are said to be congruent modulo n if (a mod n) = (b mod n). We then proved that a $\equiv$ b (mod n) if n (a - b). Some texts on number theory use this latter relationship as the definition of congruence: Two integers a and b are said to be congruent modulo n if n (a - b). Using this latter definition as the starting point, prove that, if (a mod n) = (b mod n), then n divides (a - b).