The Cayley–Menger determinant is irreducible for $n\ge 3$.

D'Andrea, Carlos, and Sombra, Martín. "The Cayley–Menger determinant is irreducible for .." Sibirskij Matematicheskij Zhurnal 46.1 (2005): 90-97. <http://eudml.org/doc/52108>.

@article{DAndrea2005,
author = {D'Andrea, Carlos, Sombra, Martín},
journal = {Sibirskij Matematicheskij Zhurnal},
keywords = {homogeneous polynomial; homogeneous evaluation; isosceles simplex; content of an integer polynomial},
language = {eng},
number = {1},
pages = {90-97},
publisher = {Sibirskoe Otdelenie Rossijskoj Akademii Nauk, Institut Matematiki Im. S. L. Soboleva SO RAN, Novosibirsk; Izdatel'stvo Instituta Matematiki},
title = {The Cayley–Menger determinant is irreducible for .},
url = {http://eudml.org/doc/52108},
volume = {46},
year = {2005},
}

TY - JOUR
AU - D'Andrea, Carlos
AU - Sombra, Martín
TI - The Cayley–Menger determinant is irreducible for .
JO - Sibirskij Matematicheskij Zhurnal
PY - 2005
PB - Sibirskoe Otdelenie Rossijskoj Akademii Nauk, Institut Matematiki Im. S. L. Soboleva SO RAN, Novosibirsk; Izdatel'stvo Instituta Matematiki
VL - 46
IS - 1
SP - 90
EP - 97
LA - eng
KW - homogeneous polynomial; homogeneous evaluation; isosceles simplex; content of an integer polynomial
UR - http://eudml.org/doc/52108
ER -