8 citations · 12 across the 7 of their papers we have counts for
9 papers
Explicit bounds for the solutions of superelliptic equations over number fields
Attila Bérczes, Yann Bugeaud, Kálmán Győry +3
Let be a polynomial with coefficients in the ring of -integers of a number field , a non-zero -integer, and an integer . We consider the equation…
Multiplicative dependence of rational values modulo approximate finitely generated groups
Attila Bérczes, Yann Bugeaud, Kálmán Győry +3
In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are `close' (with respect to the Weil height) to divisi…
Multiplicative dependence among iterated values of rational functions modulo finitely generated groups
Attila Bérczes, Alina Ostafe, Igor E. Shparlinski +1
We study multiplicative dependence between elements in orbits ofalgebraic dynamical systems over number fields modulo a finitely generated multiplicative subgroup of the field. We…
On the Diophantine equation
Gökhan Soydan
Let be fixed integers. In this paper, firstly, we prove that all solutions of the equation in integers with $x,y\geq1, n…
Finiteness results for Diophantine triples with repdigit values
Attila Bérczes, Florian Luca, István Pink +1
Let be an integer and be the set of repdigits in base . Let be the set of Diophantine triples with values in $\mathcal R_…
On Simultaneous Palindromes
Attila Bérczes, Volker Ziegler
A palindrome in base is an integer that remains the same when its digit expansion in base is reversed. Let and be given distinct integers . In this paper we…
Effective results for Diophantine equations over finitely generated domains
Attila Bérczes, Jan-Hendrik Evertse, Kálmán Györy
Let A be an arbitrary integral domain of characteristic 0 which is finitely generated over Z. We consider Thue equations with unknowns x,y from A and hyper- and superell…
Effective results for hyper- and superelliptic equations over number fields
Attila Bérczes, Jan-Hendrik Evertse, Kálmán Györy
We consider hyper- and superelliptic equations with unknowns x,y from the ring of S-integers of a given number field K. Here, f is a polynomial with S-integral coeffici…
Multiply monogenic orders
Attila Bérczes, Jan-Hendrik Evertse, Kálmán Győry
Let O be an order in an algebraic number field K, i.e., a ring with quotient field K which is contained in the ring of integers of K. The order O is called monogenic, if it is of t…