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On the spacing between terms of generalized Fibonacci sequences

Diego Marques (2014)

Colloquium Mathematicae

For k ≥ 2, the k-generalized Fibonacci sequence ( F ( k ) ) is defined to have the initial k terms 0,0,...,0,1 and be such that each term afterwards is the sum of the k preceding terms. We will prove that the number of solutions of the Diophantine equation F ( k ) - F ( ) = c > 0 (under some weak assumptions) is bounded by an effectively computable constant depending only on c.

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