Repdigits as Product of Terms of k-Bonacci Sequences
Keyword(s):
For any integer k≥2, the sequence of the k-generalized Fibonacci numbers (or k-bonacci numbers) is defined by the k initial values F−(k−2)(k)=⋯=F0(k)=0 and F1(k)=1 and such that each term afterwards is the sum of the k preceding ones. In this paper, we search for repdigits (i.e., a number whose decimal expansion is of the form aa…a, with a∈[1,9]) in the sequence (Fn(k)Fn(k+m))n, for m∈[1,9]. This result generalizes a recent work of Bednařík and Trojovská (the case in which (k,m)=(2,1)). Our main tools are the transcendental method (for Diophantine equations) together with the theory of continued fractions (reduction method).
1980 ◽
Vol 11
(2)
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pp. 197-200
2005 ◽
Vol 20
(20n21)
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pp. 4797-4819
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2012 ◽
Vol 160
(9)
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pp. 1399-1405
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Keyword(s):
2000 ◽
Vol 43
(2)
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pp. 218-225
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