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Linear forms in two logarithms and Schneider's method. II [PDF]

Acta Arithmetica, 1989
Verf. verfeinern ihre in [Acta Arith. 53, No.3, 251-287 (1989; Zbl 0642.10034)] erhaltene untere Abschätzung für \(| b_ 1 \log \alpha_ 1-b_ 2 \log \alpha_ 2| \neq 0\) bei algebraischen \(\alpha_ j\neq 0\) und ganzrationalen \(b_ j\). Dazu kombinieren sie ihre a.a.O. entwickelte Methode mit einer Technik, die sie bereits in [Math. Ann.
Mignotte, Maurice, Waldschmidt, Michel
openaire   +2 more sources

Padovan and Perrin numbers of the form 7ᵗ-5ᶻ-3ʸ-2ˣ [PDF]

Notes on Number Theory and Discrete Mathematics
Consider the Padovan sequence (pₙ)ₙ≥₀ given by pₙ₊₃=pₙ₊₁+pₙ with p₀=p₁=p₂=1. Its companion sequence, the Perrin sequence (℘ₙ)ₙ≥₀, follows the same recursive formula as the Padovan numbers, but with different initial values: p₀=3, p₁=0 and p₂=2.
Djamel Bellaouar, Özen Özer, Noureddine Azzouza   +2 more
doaj   +1 more source

Common values of two k-generalized Pell sequences [PDF]

Notes on Number Theory and Discrete Mathematics
Let k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar, Florian Luca, Faith Shadow Zottor   +2 more
doaj   +1 more source

Perfect Powers in Smarandache Type Expressions [PDF]

, 2004
The author showed that there are only finitely many numbers of the above form which are products of ...
Luca, Florian
core   +1 more source

On sums of k-generalized Fibonacci and k-generalized Lucas numbers as first and second kinds of Thabit numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Let (Fᵣ⁽ᵏ⁾)ᵣ≥2-k and (Lᵣ⁽ᵏ⁾)ᵣ≥2-k be generalizations of the Fibonacci and Lucas sequences, where k≥2. For these sequences the initial k terms are 0,0,...,0, 1 and 0,0,...,2,1, and each subsequent term is the sum of the preceding k terms.
Hunar Sherzad Taher, Saroj Kumar Dash
doaj   +1 more source

Effective irrationality measures for quotients of logarithms of rational numbers [PDF]

, 2015
We establish uniform irrationality measures for the quotients of the logarithms of two rational numbers which are very close to 1. Our proof is based on a refinement in the theory of linear forms in logarithms which goes back to a paper of ...
Bugeaud, Yann
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Linear forms in Lucas numbers [PDF]

, 1993
If (um)m∈N0 denotes a Lucas sequence, i.e. a binary integer recurrence sequence with initial values u0=0 and u1=1, then the equation kum=lun with k,l∈Z⧹{0} and max{m,n}≥5 can be valid only for finitely many Lucas sequences with coprime roots and finitely
Töpfer, Thomas
core   +1 more source

Repdigits as Euler functions of Lucas numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
We prove some results about the structure of all Lucas numbers whose Euler function is a repdigit in base 10. For example, we show that if Ln is such a Lucas number, then n < 10111 is of the form p or p2, where p3 | 10p-1 -1.
Bravo Jhon J., Faye Bernadette, Luca Florian, Tall Amadou   +3 more
doaj   +1 more source

Diophantine Equation in Logarithms [PDF]

, 2023
The main work of these pages is written by myself under the supervisor of Dr. Omar Kihel, pertaining to continued fractions and applications , linear form in logarithms and the solutions of Diophantine equation Fn1 + Fn2 + Fn3 + Fn4 = 6a .
Tian, Zhao
core   +1 more source

Modular Galois representations and linear forms in abelian logarithms [PDF]

, 2022
Les travaux de cette thèse portent sur l’étude des propriétés des représentations galoisiennes attachées aux formes modulaires et sur la théorie des formes linéaires de logarithmes abéliens.
Peaucelle, Baptiste
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