A Binomial Diophantine Equation

Weger, de Bmm Benne

doi:10.1093/qmath/47.2.221

Cited by 22 publications

(17 citation statements)

References 4 publications

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“…For more details and related results we refer to the survey paper [29] of Győry and Pintér. and for the resolution of this equation see [19] and [42]. In the case (m, n) = (2, 3) we obtain…”

Section: Family 1 Equationmentioning

confidence: 99%

Equal values of standard counting polynomials

Győry¹,

Kovàcs²,

Péter³

2014

Publ. Math. Debrecen

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The following discrete geometrical question provides a background for some classical diophantine problems. For given positive integers m, n, can an mdimensional and an n-dimensional unit cube, simplex, pyramid or octahedron contain equally many integral points? Apart from some trivial cases, the question leads to 9 families of diophantine equations, see Table 1. In this paper we give a brief survey of known results on these equations, and prove some new theorems concerning the solutions.

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Section: Family 1 Equationmentioning

confidence: 99%

Equal values of standard counting polynomials

Győry¹,

Kovàcs²,

Péter³

2014

Publ. Math. Debrecen

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“…Let J(Q) be the Jacobian of the genus two curve (8). Using MAGMA [2] we get that J(Q) is free of rank 2 with Mordell-Weil basis given by…”

Section: Proof Of Theorem 22 Observe That Equation (1) Can Be Rewrimentioning

confidence: 99%

“…the Xth figurate number with parameters k and m. For some problems and theorems related to these families of combinatorial numbers, we refer to the books [11] and [10]. The power and equal values of special cases of f k,m (X), including, for instance, binomial coefficients (for m = 3), polygonal numbers (for k = 2) and pyramidal numbers (for k = 3) have been studied intensively, see [1], [20], [4], [23], [8], [9], [14], [18], [19], [17], [16] and references therein. Brindza, Pintér and Turjányi [5] conjectured that apart from the case (m, n) = (5, 4) the equation f 3,m (x) = f 2,n (y) has only finitely many solutions in integers x, y which can be effectively determined.…”

Section: Introductionmentioning

confidence: 99%

Equal values of figurate numbers

Hajdu¹,

Tengely²,

Varga

2014

Journal of Number Theory

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“…x n = y 2 has been investigated by several authors, for general effective finiteness statements we refer to Kiss [17] and Brindza [6]. In the special cases m = 3, 4, 5 and 6, the corresponding diophantine equations were resolved by Avanesov [1], Pintér [19] and de Weger [23] (independently), Bugeaud, Mignotte, Stoll, Siksek, Tengely [8] and Hajdu, Pintér [13], respectively. The equal values of polygonal and pyramidal numbers were studied by Brindza, Pintér, Turjányi [7] and Pintér, Varga [20].…”

Section: Letmentioning

confidence: 99%