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\begin{aligned} \prod_{j\in i}(\omega+(i+1)^j) & = (\omega+1)\cdot(\omega+(i+1))\cdot(\omega+(i+1)^2)\cdot\cdots\cdot(\omega+(i+1)^{i-1}) \\ & = \omega^i+\text{ne\v{s}to} \end{aligned}
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