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Lower bounds for perfect rational cuboids. (English) Zbl 0771.11016
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)

11D09 Quadratic and bilinear Diophantine equations
11Y50 Computer solution of Diophantine equations
11D72 Diophantine equations in many variables
Full Text: EuDML
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