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Existence of a solution to a system of Diophantine Inequalities

Does the solution to the following system of inequalities exist? $$a-1\geq a\left( b_ic -d_i\right)\geq 1$$ where $a\in \mathbb{N}_{\geq3}$, $c\in \mathbb{R}$ and $b_i,d_i \in \mathbb{N}$. Moreover …
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