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Unfortunately, I also do not know how to embed 0-1-knapsack specific inequalities with the odd number solution requirement. However, I know how to generate cuts that will reduce the search space whenever an even number of items is picked. So, let $x^{*} \in \mathbb{R}^{n}$ be an optimal, eventually fractional, solution. If $\sum_{j} x^{*}_j$ is an integer ...


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