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The question is: prove that there is a bijection between sets A and B for all $n_{1}, n_{2}\in \mathbb N_{> 0}$ and for all $k_{1}, k_{2}\in \mathbb{Z}$

$A = \left\{ {n_{1}q + k_{1}} \mid q\in \mathbb{Z}\right\}$,

$B = \left\{ {n_{2}q + k_{2}} \mid q\in \mathbb{Z}\right\}$

Any help to define the function between both sets is appreciated !!

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    $\begingroup$ What are your thoughts so far? Have you tried some candidates? $\endgroup$ – T. Eskin May 1 '14 at 23:35
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HINT: Try to find a bijection of $A$ with $\Bbb Z$, for a concrete pair of $n,k$ (for example $n=2$ and $k=1$). Then try to see how that would generalize to a bijection between $A$ and $B$.

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