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Displaying 241 – 260 of 1341

The difficulty of the local solubility problem for additive equations

Trevor D. Wooley (2003)

Acta Arithmetica

The digamma function, Euler-Lehmer constants and their p-adic counterparts

T. Chatterjee, S. Gun (2014)

Acta Arithmetica

The goal of this article is twofold. First, we extend a result of Murty and Saradha (2007) related to the digamma function at rational arguments. Further, we extend another result of the same authors (2008) about the nature of p-adic Euler-Lehmer constants.

The digits of 1/p in connection with class number factors

Kurt Girstmair (1994)

Acta Arithmetica

The dilogarithm and the norm residue symbol

Robert F. Coleman (1981)

Bulletin de la Société Mathématique de France

The dimension of some affine Deligne–Lusztig varieties

Eva Viehmann (2006)

Annales scientifiques de l'École Normale Supérieure

The Dimension of the Spaces of Cusp Forms on Siegel Upper Half Plane of Degree Two.

Ki-ichiro Hasimoto (1984)

Mathematische Annalen

The dimensions of integral points and holomorphic curves on the complements of hyperplanes

Aaron Levin (2008)

Acta Arithmetica

The Diophantine Equation ...

L.J. Mordell (1967)

Mathematische Annalen

The Diophantine equation $a x^{2} + 2 b x y - 4 a y^{2} = \pm 1$ .

Bapoungué, Lionel (2003)

International Journal of Mathematics and Mathematical Sciences

The diophantine equation $a x^{2} + b x y + c y^{2} = N, D = b^{2} - 4 a c > 0$

Keith Matthews (2002)

Journal de théorie des nombres de Bordeaux

We make more accessible a neglected simple continued fraction based algorithm due to Lagrange, for deciding the solubility of $a x^{2} + b x y + c y^{2} = N$ in relatively prime integers $x, y$ , where $N \neq 0$ , gcd $(a, b, c) = gcd (a, N) = 1 et D = b^{2} - 4 a c > 0$ is not a perfect square. In the case of solubility, solutions with least positive y, from each equivalence class, are also constructed. Our paper is a generalisation of an earlier paper by the author on the equation $x^{2} - D y^{2} = N$ . As in that paper, we use a lemma on unimodular matrices that gives a much simpler proof than Lagrange’s for...

The Diophantine equation $A X^{2} - B Y^{2} = C$ solved via continued fractions.

Mollin, R.A., Cheng, K., Goddard, B. (2002)

Acta Mathematica Universitatis Comenianae. New Series

The Diophantine equation ${(b n)}^{x} + {(2 n)}^{y} = {((b + 2) n)}^{z}$

Min Tang, Quan-Hui Yang (2013)

Colloquium Mathematicae

Recently, Miyazaki and Togbé proved that for any fixed odd integer b ≥ 5 with b ≠ 89, the Diophantine equation $b^{x} + 2^{y} = {(b + 2)}^{z}$ has only the solution (x,y,z) = (1,1,1). We give an extension of this result.

The Diophantine equation $D x ² + 2^{2 m + 1} = y ⁿ$

J. H. E. Cohn (2003)

Colloquium Mathematicae

It is shown that for a given squarefree positive integer D, the equation of the title has no solutions in integers x > 0, m > 0, n ≥ 3 and y odd, nor unless D ≡ 14 (mod 16) in integers x > 0, m = 0, n ≥ 3, y > 0, provided in each case that n does not divide the class number of the imaginary quadratic field containing √(-2D), except for a small number of (stated) exceptions.

The diophantine equation $d y^{2} = a x^{4} + b x^{2} + c$

L. Mordell (1969)

Acta Arithmetica

The Diophantine equation f(x) = g(y)

Yuri Bilu, Robert Tichy (2000)

Acta Arithmetica

The diophantine equation $n^{i} + 1 = k (d n - 1)$ .

Ligh, Steve, Bourque, Keith (1989)

International Journal of Mathematics and Mathematical Sciences

The diophantine equation $r^{2} + r (x + y) = k x y$ .

Utz, W.R. (1985)

International Journal of Mathematics and Mathematical Sciences

The diophantine equation $x^{2} + 2^{a} \cdot 17^{b} = y^{n}$

Su Gou, Tingting Wang (2012)

Czechoslovak Mathematical Journal

Let $ℤ$ , $ℕ$ be the sets of all integers and positive integers, respectively. Let $p$ be a fixed odd prime. Recently, there have been many papers concerned with solutions $(x, y, n, a, b)$ of the equation $x^{2} + 2^{a} p^{b} = y^{n}$ , $x, y, n \in ℕ$ , $gcd (x, y) = 1$ , $n \geq 3$ , $a, b \in ℤ$ , $a \geq 0$ , $b \geq 0 .$ And all solutions of it have been determined for the cases $p = 3$ , $p = 5$ , $p = 11$ and $p = 13$ . In this paper, we mainly concentrate on the case $p = 3$ , and using certain recent results on exponential diophantine equations including the famous Catalan equation, all solutions $(x, y, n, a, b)$ of the equation $x^{2} + 2^{a} \cdot 17^{b} = y^{n}$ , $x, y, n \in ℕ$ , $gcd (x, y) = 1$ , $n \geq 3$ , $a, b \in ℤ$ , $a \geq 0$ , $b \geq 0$ , are determined....

The Diophantine equation $x^{2} + 2^{k} = y^{n}$ . II.

Cohn, J.H.E. (1999)

International Journal of Mathematics and Mathematical Sciences

The diophantine equation $x^{2} + 3^{m} = y^{n}$ .

Arif, S.Akhtar, Abu Muriefah, Fadwa S. (1998)

International Journal of Mathematics and Mathematical Sciences

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