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<p>The problem is concretely about Boolean functions $latex {f}$ of $latex {k}$ variables, and seems not to involve prime numbers at all.  For any subset $latex {S}$ of the coordinates, the corresponding Fourier coefficient is given by:</p>

<p>The problem is concretely about Boolean functions <math>f\!</math> of <math>k\!</math> variables, and seems not to involve prime numbers at all.  For any subset <math>S\!</math> of the coordinates, the corresponding Fourier coefficient is given by:</p>

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<p align="center"><math>\hat{f}(S) = \frac{1}{2^k} \sum_{x \in \mathbb{Z}_2^k} f(x)\chi_S(x)\!</math></p>

<math>\displaystyle \hat{f}(S) = \frac{1}{2^k} \sum_{x \in \mathbb{Z}_2^k} f(x)\chi_S(x)\!</math>

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<p>where <math>\chi_S(x)\!</math> is <math>-1\!</math> if <math>\sum_{i \in S} x_i\!</math> is odd, and <math>+1\!</math> otherwise.</p>

<p>where <math>\chi_S(x)\!</math> is <math>-1\!</math> if <math>\textstyle \sum_{i \in S} x_i\!</math> is odd, and <math>+1\!</math> otherwise.</p>

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