Výsledky vyhledávání - "Mignotte, M."

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On $px^2 + q^{2n}= y^p$ and related Diophantine equations

Autor: Laradji, A., Mignotte, M., Tzanakis, N.

Publikováno v: Journal of Number Theory 131 (2011), 1575-1596

The title equation, where $p>3$ is a prime number $\not\equiv 7 \pmod 8$, $q$ is an odd prime number and $x,y,n$ are positive integers with $x,y$ relatively prime, is studied. When $p\equiv 3\pmod 8$, we prove (Theorem 2.3) that there are no solution

Externí odkaz: http://arxiv.org/abs/1002.1041

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Elementary Trigonometric Sums related to Quadratic Residues

Autor: Laradji, A., Mignotte, M., Tzanakis, N.

Let p be a prime = 3 (mod 4). A number of elegant number-theoretical properties of the sums T(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} tan(n^2\pi/p) and C(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} cot(n^2\pi/p) are proved. For example, T(p) equals p times the excess

Externí odkaz: http://arxiv.org/abs/1001.2638

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Integral Points on Hyperelliptic Curves

Autor: Bugeaud, Y., Mignotte, M., Siksek, S., Stoll, M., Tengely, Sz.

Publikováno v: Algebra & Number Theory 2 (2008), No. 8, 859-885.

We give a completely explicit upper bound for integral points on (standard) affine models of hyperelliptic curves, provided we know at least one rational point and a Mordell-Weil basis of the Jacobian. We also explain a powerful refinement of the Mor

Externí odkaz: http://arxiv.org/abs/0801.4459

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