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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 153–160 (Mi ufa141)  

This article is cited in 1 scientific paper (total in 1 paper)

Perfect cuboids and irreducible polynomials

R. A. Sharipov

Bashkir State University, Ufa, Russia

Abstract: 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 $u$.

Keywords: an Euler cuboid, a perfect cuboid, irreducible polynomials.

Full text: PDF file (397 kB)
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UDC: 511.515+511.54+512.752
Received: 02.09.2011

Citation: R. A. Sharipov, “Perfect cuboids and irreducible polynomials”, Ufimsk. Mat. Zh., 4:1 (2012), 153–160

Citation in format AMSBIB
\Bibitem{Sha12}
\by R.~A.~Sharipov
\paper Perfect cuboids and irreducible polynomials
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 153--160
\mathnet{http://mi.mathnet.ru/ufa141}


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    This publication is cited in the following articles:
    1. R. A. Sharipov, “Asymptotic approach to the perfect cuboid problem”, Ufa Math. J., 7:3 (2015), 95–107  mathnet  crossref  isi  elib
  • Уфимский математический журнал
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