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I give a $\mathbf{\text{positive}}$ answer to my own question, thanks to How to show that the integral $\frac{1}{2\pi i} \int_{\gamma} \frac{dz}{z - a}$ is integer-valued when the curve $\gamma$ is not piecewise smooth?. In the beginning, I post here some main statements which we will observe in detail later: statement 1 Let $\epsilon$ be an ...