Homework Sheet 2 Congruence on Numbers modulom by vqx13199

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									Homework Sheet 2: Congruence on Numbers modulo m
 1. Let m ∈ N. Consider the congruence relation ≡m on Z. Show that
     (a) If x ≡m a, y ≡m b, then x + y ≡m a + b.
    (b) If x ≡m a, y ≡m b, then xy ≡m ab.
 2. Define a relation on A = {0, 1, 2, 3, 4, 5, 6, 7} such that aRb if and only if
    8 | a2 − b 2 .

     (a) Prove that R is an equivalence relation.
    (b) Write down the partition of A given by R.




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