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We consider the Tribonacci sequence given by T₀ = 0, T₁ = T₂ = 1 and for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.
Carlos Alexis Ruiz Gómez, and Florian Luca. "Multiplicatively dependent triples of Tribonacci numbers." Acta Arithmetica 171.4 (2015): 327-353. <http://eudml.org/doc/279239>.
@article{CarlosAlexisRuizGómez2015, abstract = {We consider the Tribonacci sequence $T:= \{T_n\}_\{n≥0\}$ given by T₀ = 0, T₁ = T₂ = 1 and $T_\{n+3\} = T_\{n+2\} + T_\{n+1\} + T_n$ for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.}, author = {Carlos Alexis Ruiz Gómez, Florian Luca}, journal = {Acta Arithmetica}, keywords = {multiplicatively independent integers; tribonacci numbers; linear forms in logarithms of algebraic numbers}, language = {eng}, number = {4}, pages = {327-353}, title = {Multiplicatively dependent triples of Tribonacci numbers}, url = {http://eudml.org/doc/279239}, volume = {171}, year = {2015}, }
TY - JOUR AU - Carlos Alexis Ruiz Gómez AU - Florian Luca TI - Multiplicatively dependent triples of Tribonacci numbers JO - Acta Arithmetica PY - 2015 VL - 171 IS - 4 SP - 327 EP - 353 AB - We consider the Tribonacci sequence $T:= {T_n}_{n≥0}$ given by T₀ = 0, T₁ = T₂ = 1 and $T_{n+3} = T_{n+2} + T_{n+1} + T_n$ for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent. LA - eng KW - multiplicatively independent integers; tribonacci numbers; linear forms in logarithms of algebraic numbers UR - http://eudml.org/doc/279239 ER -