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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.

I need to prove that:

a) R is an equivalence relation. (which I have)

b) 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

I can use the following lemma to prove b: "If p is prime and p|mn, then p|m or p|n"

Could you show me how to prove b? Preferably with as many steps as possible so it's clear what's happening in each step?

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