Article
Ufa Mathematical Journal
Volume 4, Number 1, pp. 143-150
Perfect cuboids and irreducible polynomials.
Sharipov R. A.
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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 $10\,000$ instances of $a$, $b$, and $u$.