Currently displaying 1 – 19 of 19

Showing per page

Order by Relevance | Title | Year of publication

Sur les carrés dans certaines suites de Lucas

Maurice Mignotte;  Attila Pethö — 1993

Journal de théorie des nombres de Bordeaux

Soit a un entier ≥ 3 . Pour α = ( a + a 2 - 4 ) / 2 et β = ( a - a 2 - 4 ) / 2 , nous considérons la suite de Lucas 𝑢 𝑛 = ( α 𝑛 - β 𝑛 ) / ( α - β ) . Nous montrons que, pour a ≥ 4 , 𝑢 𝑛 n’est ni un carré, ni le double, ni le triple d’un carré, ni six fois un carré pour n > 3 sauf si a = 338 et n = 4 .

Effective bounds for the zeros of linear recurrences in function fields

Clemens Fuchs;  Attila Pethő — 2005

Journal de Théorie des Nombres de Bordeaux

In this paper, we use the generalisation of Mason’s inequality due to Brownawell and Masser (cf. [8]) to prove effective upper bounds for the zeros of a linear recurring sequence defined over a field of functions in one variable. Moreover, we study similar problems in this context as the equation G n ( x ) = G m ( P ( x ) ) , ( m , n ) ∈ ℕ 2 , where ( G n ( x ) ) is a linear recurring sequence of polynomials and P ( x ) is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].

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

Maurice Mignotte;  Attila Petho — 1999

Publicacions Matemàtiques

We consider the diophantine equation (*)    xp - x = yq - 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.

Bases of canonical number systems in quartic algebraic number fields

Horst Brunotte;  Andrea Huszti;  Attila Pethő — 2006

Journal de Théorie des Nombres de Bordeaux

Canonical number systems can be viewed as natural generalizations of radix representations of ordinary integers to algebraic integers. A slightly modified version of an algorithm of and is presented here for the determination of canonical number systems in orders of algebraic number fields. Using this algorithm canonical number systems of some quartic fields are computed.

Finite and periodic orbits of shift radix systems

Peter Kirschenhofer;  Attila Pethő;  Paul Surer;  Jörg Thuswaldner — 2010

Journal de Théorie des Nombres de Bordeaux

For r = ( r 0 , ... , r d - 1 ) ∈ ℝ d define the function τ r : ℤ d → ℤ d , z = ( z 0 , ... , z d - 1 ) ↦ ( z 1 , ... , z d - 1 , - rz ) , where rz is the scalar product of the vectors r and z . If each orbit of τ r ends up at 0 , we call τ r a shift radix system. It is a well-known fact that each orbit of τ r ends up periodically if the polynomial t d + r d - 1 t d - 1 + ⋯ + r 0 associated to r is contractive. On the other hand, whenever this polynomial has at least one root outside the unit disc, there exist starting vectors that give rise to unbounded orbits. The present paper deals with the...

Page 1

Download Results (CSV)