# Its hip to be skew

Show that the determinant of a skew symmetric $2n\times 2n$ matrix is never reducible when viewed as a polynomial in $\binom {2n} 2$ variables.

# One step forward, two steps back

Let $f:\mathbb{R}\to\mathbb{R}$ be an infinitely differentiable function. Does there existe $g:\mathbb R\to\mathbb R$ also infinitely differentiable such that $f(x) = g(x+1)-g(x)$ for all $x\in\mathbb R$?