Parametric solutions for some Diophantine equations.

Andrica, Dorin; Tudor, Gheorghe M.

Displaying similar documents to “Parametric solutions for some Diophantine equations.”

Ljunggren's Diophantine problem connected with virus structure.

Grytczuk, Aleksander (2006)

Annales Mathematicae et Informaticae

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On Bumby’s equation ${(x^{2} - 2)}^{2} - 2 = 2 y^{2}$ : a solution via pythagorean triples

Ladislav Beran (1987)

Acta Universitatis Carolinae. Mathematica et Physica

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On Lucas and Lehmer sequences and their applications to Diophantine equations

K. Györy, P. Kiss, A. Schinzel (1981)

Colloquium Mathematicae

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Diophantine equation $\frac{q^{n} - 1}{q - 1} = y$ for four prime divisors of $y - 1$

Zdeněk Polický (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper the special diophantine equation $\frac{q^{n} - 1}{q - 1} = y$ with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of $y - 1$ .

A generalization of the question of Sierpiński on geometric progressions.

Luo, Jiagui, Yuan, Pingzhi (2010)

Journal of Integer Sequences [electronic only]

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

Utz, W.R. (1985)

International Journal of Mathematics and Mathematical Sciences

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On the Diophantine equation x² - dy⁴ = 1 with prime discriminant II

D. Poulakis, P. G. Walsh (2006)

Colloquium Mathematicae

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Let p denote a prime number. P. Samuel recently solved the problem of determining all squares in the linear recurrence sequence {Tₙ}, where Tₙ and Uₙ satisfy Tₙ² - pUₙ² = 1. Samuel left open the problem of determining all squares in the sequence {Uₙ}. This problem was recently solved by the authors. In the present paper, we extend our previous joint work by completely solving the equation Uₙ = bx², where b is a fixed positive squarefree integer. This result also extends previous work...

On sets S.

P. Laborde (1970)

Gaceta Matemática

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Parametric Solutions of the Diophantine Equation A² + nB⁴ = C³

Susil Kumar Jena (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.