Powers of Two in Generalized Fibonacci Sequences
The k-generalized Fibonacci sequence \big(Fn(k)\big)n resembles the Fibonacci sequence in that it starts with 0,…,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we are interested in finding powers of two that appear in k-generalized Fibonacci sequences; i.e., we study the Diophantine equation Fn(k)=2m in positive integers n,k,m with k≥ 2.
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2012
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oai:scielo:S0034-742620120001000052014-04-08Powers of Two in Generalized Fibonacci SequencesBRAVO,JHON J.LUCA,FLORIAN Fibonacci numbers Lower bounds for nonzero linear forms in logarithms of algebraic numbers The k-generalized Fibonacci sequence \big(Fn(k)\big)n resembles the Fibonacci sequence in that it starts with 0,…,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we are interested in finding powers of two that appear in k-generalized Fibonacci sequences; i.e., we study the Diophantine equation Fn(k)=2m in positive integers n,k,m with k≥ 2.info:eu-repo/semantics/openAccessUniversidad Nacional de Colombia y Sociedad Colombiana de MatemáticasRevista Colombiana de Matemáticas v.46 n.1 20122012-06-01info:eu-repo/semantics/articletext/htmlhttp://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262012000100005en |
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BRAVO,JHON J. LUCA,FLORIAN |
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BRAVO,JHON J. LUCA,FLORIAN Powers of Two in Generalized Fibonacci Sequences |
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BRAVO,JHON J. LUCA,FLORIAN |
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BRAVO,JHON J. |
| title |
Powers of Two in Generalized Fibonacci Sequences |
| title_short |
Powers of Two in Generalized Fibonacci Sequences |
| title_full |
Powers of Two in Generalized Fibonacci Sequences |
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Powers of Two in Generalized Fibonacci Sequences |
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Powers of Two in Generalized Fibonacci Sequences |
| title_sort |
powers of two in generalized fibonacci sequences |
| description |
The k-generalized Fibonacci sequence \big(Fn(k)\big)n resembles the Fibonacci sequence in that it starts with 0,…,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we are interested in finding powers of two that appear in k-generalized Fibonacci sequences; i.e., we study the Diophantine equation Fn(k)=2m in positive integers n,k,m with k≥ 2. |
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Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas |
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2012 |
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http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262012000100005 |
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AT bravojhonj powersoftwoingeneralizedfibonaccisequences AT lucaflorian powersoftwoingeneralizedfibonaccisequences |
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