In Section 4.3, we define the congruence relationship as follows: Two integers \(a\) and \(b\) are said to be congruent modulo \(n\) if \((a \bmod n)=(b \bmod n)\). We then proved that \(a \equiv b(\bmod n)\) if \(n \mid(a-b)\). 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 \(n \mid(a-b)\). Using this latter definition as the starting point, prove that, if \((a \bmod n)=(b \bmod n)\), then \(n\) divides \((a-b)\).