Abstract: How many degree d polynomials $f \in \mathbb{R}[x_1, x_2, \ldots, x_n]$ are irreducible over $\mathbb{R}$? We will use topology to give this question an interesting interpretation, and then use number theory and combinatorics to express the number of $\mathbb{R}$-irreducible polynomials in terms of the binary digits of n, the number of variables.
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