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for question related to conjectures.
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A conjecture on intersection of some intervals.
It was proved here that if $a\in \mathbb{N}_{\geq3}$ then
$$\bigcap_{i = 1}^{a} \bigcup_{j = 0}^{i-1} \left[\frac{1+aj}{i},\frac{a(j+1)-1}{i}\right] = \varnothing \tag{1}$$
It may be conjectured tha …