Irreducibility of the Cayley-Menger determinant, and of a class of related polynomials

Mowaffaq Hajja, Mostafa Hayajneh, Bach Nguyen +1

If $S$ is a given regular $n$-simplex, $n\ge 2$, of edge length $a$, then the distances $a_1$, $\cdots$, $a_{n+1}$ of an arbitrary point in its affine hull to its vertices are rel…