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Let p and q be any two distinct prime numbers and define the relation a R...

Let p and q be any two distinct prime numbers and define the relation a R b on integers a,b by: a R b iff b-a is divisible by both p and q. For this relation R: Show that the equivalence classes of R correspond to the elements of  ℤpq. That is: [a] = [b] as equivalence classes of R if and only if [a] = [b] as elements of ℤpq.

you may use the following lemma: If p is prime and p|mn, then p|m or p|n. Indicate in your proof the step(s) for which you invoke this lemma.

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