/sci/ - Science & Math

[math]
\text{Find necessary and sufficient conditions on positive integers }m\text{ and }n\text{ so that}
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\qquad \qquad \qquad \qquad \qquad \sum_{i=0}^{mn-1} (-1)^{\lfloor i/m \rfloor +\lfloor i/n\rfloor}=0.
[/math]