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- Attila Pethö, Robert F. Tichy
- J. Symb. Comput.
- 1998

Two-parametric quartic Thue equations are completely solved for sufficiently large values of the parameters. Exceptional units are computed in related quartic number fields. The method depends… (More)

- Attila Pethö
- J. Symb. Comput.
- 1987

- Shigeki Akiyama, Attila Pethö
- Theor. Comput. Sci.
- 2002

Let P (x) = pdx + . . . + p0 ∈ Z[x] be such that d ≥ 1, pd = 1, p0 ≥ 2 and N = {0, 1, . . . , p0 − 1}. We are proving in this note a new criterion for the pair {P (x),N} to be a canonical number… (More)

- Josef Gebel, Attila Pethö, Horst Günter Zimmer
- ANTS
- 1996

By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demjanenko [L3] states that, for a… (More)

- Maurice Mignotte, Attila Pethö, Ralf Roth
- Math. Comput.
- 1996

Continuing the recent work of the second author, we prove that the diophantine equation fa(x, y) = x 4 − axy − xy + axy + y = 1 for |a| ≥ 3 has exactly 12 solutions except when |a| = 4, when it has… (More)

- Shigeki Akiyama, Horst Brunotte, Attila Pethö
- Periodica Mathematica Hungarica
- 2007

The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators… (More)

- István Gaál, Attila Pethö, Michael E. Pohst
- ISSAC
- 1991

is soluble and to compute all solutions of (2) to find all integral elements with least index. The problem of solving (1) was worked out by Gad and Schulte [3] for cubic number fields and by Gad,… (More)

- Shigeki Akiyama, Horst Brunotte, Attila Pethö, Wolfgang Steiner
- Periodica Mathematica Hungarica
- 2006

The periodicity of sequences of integers (an)n∈Z satisfying the inequalities 0 ≤ an−1 + λan + an+1 < 1 (n ∈ Z) is studied for real λ with |λ| < 2. Periodicity is proved in case λ is the golden ratio;… (More)

- Clemens Heuberger, Attila Pethö, Robert F. Tichy
- J. Symb. Comput.
- 2002

We completely solve the family of relative Thue equations x 3 − (t − 1)xy − (t + 2)xy − y = μ, where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary… (More)

- István Gaál, Attila Pethö, Michael E. Pohst
- J. Symb. Comput.
- 1993

In this paper we develop a method for computing all small solutions (i.e. with coordinates of absolute value < 10’) of index form equations in totally real biquadratic number fields. If the index… (More)