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On the number of terms with odd coefficients

Source: 2018 Thailand October Camp 3.3

February 19, 2022
algebrapolynomialcoefficientscombinatorics

Problem Statement

Let n≥2n\geq 2 be an integer. Determine the number of terms in the polynomial ∏1≤i<j≤n(xi+xj)\prod_{1\leq i< j\leq n}(x_i+x_j) whose coefficients are odd integers.
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