A note on the first cuboid conjecture

Sharipov, Ruslan

doi:10.48550/arxiv.1109.2534

Cited by 9 publications

(11 citation statements)

References 2 publications

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“…A similar theorem associated with the first cuboid conjecture was formulated and proved in [2]. A similar theorem associated with the second cuboid conjecture was formulated in [3].…”

Section: Introductionmentioning

confidence: 65%

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A note on the third cuboid conjecture. Part I

Sharipov

2012

Preprint

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The problem of finding perfect Euler cuboids or proving their nonexistence is an old unsolved problem in mathematics. The third cuboid conjecture is the last of the three propositions suggested as intermediate stages in proving the non-existence of perfect Euler cuboids. It is associated with a certain Diophantine equation of the order 12. In this paper a structural theorem for the solutions of this Diophantine equation is proved.Conjecture 1.1 (third cuboid conjecture). For any three positive coprime integer numbers a, b, and u such that none of the conditions (1.2) is satisfied the polynomialThe subcases 2, 5, and 6 in (1.2) are trivial. The subcase 1 leads to the first cuboid conjecture. The subcases 3 and 4 lead to the second cuboid conjecture. The first, the second, and the third cuboid conjectures were introduced [1]. They

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“…A similar theorem associated with the first cuboid conjecture was formulated and proved in [2]. A similar theorem associated with the second cuboid conjecture was formulated in [3].…”

Section: Introductionmentioning

confidence: 65%

“…The special cases (1.2) were studied in [1], [2], and [3]. In a general case other than those listed in (1.2) the polynomial (1.1) is described by the following conjecture.…”

Section: Introductionmentioning

confidence: 99%

A note on the third cuboid conjecture. Part I

Sharipov

2012

Preprint

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“…Note that a similar theorem associated with the first cuboid conjecture was formulated and proved in [38]. The theorem 1.1 is a weaker proposition than the conjecture 1.1 itself.…”

Section: Introductionmentioning

confidence: 81%

Asymptotic approach to the perfect cuboid problem

Шарипов¹

2015

Ufimskii Matematicheskii Zhurnal

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“…There are also two series of ArXiv publications. The first of them [52][53][54] continues the research on cuboid conjectures. The second one [55][56][57][58][59][60][61][62][63][64][65][66][67] relates perfect cuboids with multisymmetric polynomials.…”

Section: Introductionmentioning

confidence: 99%

A fast modulo primes algorithm for searching perfect cuboids and its implementation

Gallyamov,

Kadyrov,

Kashelevskiy

et al. 2016

Preprint

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A perfect cuboid is a rectangular parallelepiped whose all linear extents are given by integer numbers, i. e. its edges, its face diagonals, and its space diagonal are of integer lengths. None of perfect cuboids is known thus far. Their non-existence is also not proved. This is an old unsolved mathematical problem.Three mathematical propositions have been recently associated with the cuboid problem. They are known as three cuboid conjectures. These three conjectures specify three special subcases in the search for perfect cuboids. The case of the second conjecture is associated with solutions of a tenth degree Diophantine equation. In the present paper a fast algorithm for searching solutions of this Diophantine equation using modulo primes seive is suggested and its implementation on 32-bit Windows platform with Intel-compatible processors is presented.

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A note on the first cuboid conjecture

Cited by 9 publications

References 2 publications

A note on the third cuboid conjecture. Part I

A note on the third cuboid conjecture. Part I

Asymptotic approach to the perfect cuboid problem

A fast modulo primes algorithm for searching perfect cuboids and its implementation

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