These are the pairs I found $(4,1),(7,1),(5,2),(8,2),(6,3),(7,4)$
Are there any other?
Also, should pairs like $(1,4), (4,4)$ be included?
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Yes, (1,4) and (4,4) are included because they satisfy $3|i-j$ , which is an equivalent formulation to $i\equiv j\mod 3$ – Peter Nov 18 '16 at 14:24
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You forgot $(8,5)$ – Peter Nov 18 '16 at 14:25
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@Peter, So the correct answer is $(4,1),(7,1),(5,2),(8,5),(8,2),(6,3),(7,4),(1,4),(1,7),(2,5),(5,8),(2,8),(3,6),(4,7),(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8)$ – MrDi Nov 18 '16 at 14:27
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Yes, those are the pairs. – Peter Nov 18 '16 at 14:29