EUDML | On the diophantine equation xp - x = yq - y.

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Displaying similar documents to “On the diophantine equation xp - x = yq - y.”

Complete solution of a family of simultaneous Pellian equations

Andrej Dujella (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

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A class of diophantine equations connected with certain elliptic curves over $Q (\sqrt{- 13})$

R. J. Stroeker (1979)

Compositio Mathematica

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Diophantine inequalities in imaginary quadratic number fields

Robert Franz Tichy (1994)

Mathematica Slovaca

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Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms. The case of quartic equations

N. Tzanakis (1996)

Acta Arithmetica

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On two-parametric family of quartic Thue equations

Borka Jadrijević (2005)

Journal de Théorie des Nombres de Bordeaux

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We show that for all integers $m$ and $n$ there are no non-trivial solutions of Thue equation $x^{4} - 2 m n x^{3} y + 2 (m^{2} - n^{2} + 1) x^{2} y^{2} + 2 m n x y^{3} + y^{4} = 1,$ satisfying the additional condition $gcd (x y, m n) = 1$ .