Complete solution of a family of simultaneous Pellian equations

Andrej Dujella

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Displaying similar documents to “Complete solution of a family of simultaneous Pellian equations”

On the diophantine equation x - x = y - y.

Maurice Mignotte, Attila Petho (1999)

Publicacions Matemàtiques

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We consider the diophantine equation (*) x^p - x = y^q - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.

Diophantine inequalities in imaginary quadratic number fields

Robert Franz Tichy (1994)

Mathematica Slovaca

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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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Distribution of solutions of diophantine equations $f_{1} (x_{1}) f_{2} (x_{2}) = f_{3} (x_{3})$ , where $f_{i}$ are polynomials

A. Schinzel, U. Zannier (1992)

Rendiconti del Seminario Matematico della Università di Padova

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Note on a Shannon's theorem concerning the Fibonacci numbers and Diophantine quadruples

Morgado, José (1991)

Portugaliae mathematica

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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 the diophantine equation $y^{2} + D^{m} = p^{n}$

Masao Toyoizumi (1983)

Acta Arithmetica

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Displaying similar documents to “Complete solution of a family of simultaneous Pellian equations”

On the diophantine equation x - x = y - y.

Diophantine inequalities in imaginary quadratic number fields

A class of diophantine equations connected with certain elliptic curves over Q ( - 13 )

Distribution of solutions of diophantine equations f 1 ( x 1 ) f 2 ( x 2 ) = f 3 ( x 3 ) , where f i are polynomials

Note on a Shannon's theorem concerning the Fibonacci numbers and Diophantine quadruples

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

On the diophantine equation y 2 + D m = p n

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

Distribution of solutions of diophantine equations $f_{1} (x_{1}) f_{2} (x_{2}) = f_{3} (x_{3})$ , where $f_{i}$ are polynomials

On the diophantine equation $y^{2} + D^{m} = p^{n}$