A parametric family of sextic Thue equations

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 $gcd (x y, m n) = 1$ .

The number of solutions of the Thue-Mahler equation.

Jan-Hendrik Evertse (1997)

Journal für die reine und angewandte Mathematik

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Solutions to infinite families of complex cubic Thue equations.

Emery Thomas (1993)

Journal für die reine und angewandte Mathematik

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On equation in S-units and the Thue-Mahler equation.

J.H. Evertse (1984)

Inventiones mathematicae

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On a conjecture of E. Thomas concerning parametrized Thue equations

Clemens Heuberger (2001)

Acta Arithmetica

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Binary words avoided by the Thue-Morse sequence.

A.M. Shur (1996)

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Robert Tijdeman (1974-1975)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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J.H. Evertse (1984)

Inventiones mathematicae

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T. N. Shorey (1975-1976)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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