No Perfect Cuboid

Abstract

A rectangular parallelepiped is called a cuboid (standing box). It is called perfect if its edges, face diagonals and body diagonal all have integer length. Euler gave an example where only the body diagonal failed to be an integer (Euler brick). Are there perfect cuboids? We prove that there is no perfect cuboid.

Cited by in corpus (2)

• On Walter Wyss's no perfect cuboid paper
• A fast modulo primes algorithm for searching perfect cuboids and its implementation