Wyniki wyszukiwania

1

Units generating the ring of integers of complex cubic fields

100%

Tichy R., Ziegler V.

Colloquium Mathematicum

|

2007

|

tom 109

|

nr 1

71-83

EN

All purely cubic fields such that their maximal order is generated by its units are determined.

2

Multiplicative relations on binary recurrences

100%

Luca F., Ziegler V.

Acta Arithmetica

|

2013

|

tom 161

|

nr 2

183-199

EN

Given a binary recurrence ${u_n}_{n≥0}$, we consider the Diophantine equation $u_{n_1}^{x_1} ⋯ u_{n_L}^{x_L} = 1$ with nonnegative integer unknowns $n_1,..., n_L$, where $n_i ≠ n_j$ for 1 ≤ i < j ≤ L, $max{|x_i|: 1 ≤ i ≤ L} ≤ K$, and K is a fixed parameter. We show that the above equation has only finitely many solutions and the largest one can be explicitly bounded. We demonstrate the strength of our method by completely solving a particular Diophantine equation of the above form.

3

Finiteness results for Diophantine triples with repdigit values

81%

Bérczes A., Luca F., Pink I., Ziegler V.

Acta Arithmetica

|

2016

|

tom 172

|

nr 2

133-148

EN

Let g ≥ 2 be an integer and $𝓡_g ⊂ ℕ$ be the set of repdigits in base g. Let $𝓓_g$ be the set of Diophantine triples with values in $𝓡_g$; that is, $𝓓_g$ is the set of all triples (a,b,c) ∈ ℕ³ with c < b < a such that ab + 1, ac + 1 and bc + 1 lie in the set $𝓡_g$. We prove effective finiteness results for the set $𝓓_g$.

4

On the quantitative unit sum number problem-an application of the subspace theorem

81%

Filipin A., Tichy R., Ziegler V.

Acta Arithmetica

|

2008

|

tom 133

|

nr 4

297-308

Ograniczanie wyników

3 Acta Arithmetica

1 Colloquium Mathematicum

4 Ziegler V.

2 Luca F.

2 Tichy R.

1 Bérczes A.

1 Filipin A.

1 Pink I.

1 2016

1 2013

1 2008

1 2007

Units generating the ring of integers of complex cubic fields

Multiplicative relations on binary recurrences

Finiteness results for Diophantine triples with repdigit values

On the quantitative unit sum number problem-an application of the subspace theorem