Perfect cuboids and irreducible polynomials

Details Perfect cuboids and irreducible polynomials Perfect cuboids and irreducible polynomials

2011-08-26

arxiv.org/abs/1108.5348v1

Ufa Mathematical Journal, ISSN 2074-1863, Vol. 4, No. 1 (2012), P. 153-160

Mathematics

Number Theory

AmSTeX, 8 pages, amsppt style

Scientific paper

The problem of constructing a perfect cuboid is related to a certain class of univariate polynomials with three integer parameters $a$, $b$, and $u$. Their irreducibility over the ring of integers under certain restrictions for $a$, $b$, and $u$ would mean the non-existence of perfect cuboids. This irreducibility is conjectured and then verified numerically for approximately 10000 instances of $a$, $b$, and $u$.

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