4.9 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 mod n) = (b mod n). We then proved that a K 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). | |
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