Parametric Solutions for a Nearly-Perfect Cuboid
Mamuka Meskhishvili · arXiv (Cornell University) · 2015
Meskhishvili provided three rational parametrizations for nearly perfect cuboids where one face diagonal remains unresolved. This paper analyzes his second and third parametrizations and proves that the two fundamental infinite subfamilies of the associated Pell equation cannot resolve the remaining diagonal to form a non-degenerate perfect cuboid. Consequently, these specific subfamilies can be safely excluded from future computational searches. Furthermore, a definitive, explicitly testable exclusion corridor is established for the third family. All proofs rely entirely on exact polynomial identities and strict integer inequalities, avoiding any asymptotic approximations.