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The Canonical Diophantine Equations with Applications

✍ Scribed by Wolovich, W. A.; Antsaklis, P. J.


Book ID
118210511
Publisher
Society for Industrial and Applied Mathematics
Year
1984
Tongue
English
Weight
929 KB
Volume
22
Category
Article
ISSN
0363-0129

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πŸ“œ SIMILAR VOLUMES


Diophantine equations , odd graphs, and
✍ Chun-Gang Ji πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 239 KB

Let D > 2 be a square-free integer and define a direct graph G(D) such that the vertices of the graph are the primes p i dividing D, and the arcs are determined by conditions on the quadratic residues (p i /p j ). In this paper, our main result is that x 2 -Dy 2 = k, where k = -1, Β±2, is solvable if

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Let D > 2 be a positive integer, and let p be an odd prime not dividing D. In this paper, using the deep result of Bilu, Hanrot and Voutier (i.e., the existence of primitive prime factors of Lucas and Lehmer sequences), by computing Jacobi's symbols and using elementary arguments, we prove that: if

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In this paper, we prove the equation in the title has no positive integer solutions (x, y, n) with 2 | n and x = y apart from (x, y, n) = (5, 2, 5), (90, 2, 13).

On the Diophantine equation
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