Korec, Ivan Lower bounds for perfect rational cuboids. (English) Zbl 0771.11016 Math. Slovaca 42, No. 5, 565-582 (1992). A perfect rational cuboid is a cuboid in which all three edges, all three face diagonals and the body diagonal are integers. In this paper some lower bounds for a perfect rational cuboid are derived using computer computations. For example, its greatest edge must be at least \(4\cdot 10^ 9\), and its body diagonal \(z\) must be at least \(11\cdot10^ 6\cdot q\), where \(q\) is the greatest prime divisor of \(z\). Further, \(z\) can be neither a prime power nor a product of two primes. Reviewer: E.L.Cohen (Ottawa) Cited in 1 Document MSC: 11D09 Quadratic and bilinear Diophantine equations 11Y50 Computer solution of Diophantine equations 11D72 Diophantine equations in many variables Keywords:quadratic diophantine equations; perfect rational cuboid PDF BibTeX XML Cite \textit{I. Korec}, Math. Slovaca 42, No. 5, 565--582 (1992; Zbl 0771.11016) Full Text: EuDML OpenURL References: [1] KOREC I.: Nonexistence of a small perfect rational cuboid 11. Acta Math. Univ. Comen. XLIV-XLV (1984), 39-48. · Zbl 0555.10006 [2] LEECH J.: The rational cuboid revisited. Amer. Math. Monthly 84 (1977), 518-533. · Zbl 0373.10011 [3] MORDELL L. J.: Diophantine equations. Academic Press, London and New York, 1959. · Zbl 0188.34503 [4] POCKLINGTON H. O.: Some Diophantine impossibilities. Proc. Cambridge Philosophical Society 17 (1914), 108-121. · JFM 44.0234.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.