Fibonacci s-Cullen and s-Woodall numbers
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Data
2015
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The m-th Cullen number C m is a number of the form m2 m + 1 and the m-th
Woodall number W m has the form m2 m − 1. In 2003, Luca and Stănică proved that
the largest Fibonacci number in the Cullen sequence is F 4 = 3 and that F 1 = F 2 = 1
are the largest Fibonacci numbers in the Woodall sequence. Very recently, the second
author proved that, for any given s > 1, the equation F n = ms m ± 1 has only finitely
many solutions, and they are effectively computable. In this note, we shall provide the
explicit form of the possible solutions.
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CHAVES, Ana Paula; MARQUES, Diego. Fibonacci s-Cullen and s-Woodall numbers. Journal of Integer Sequences, Waterloo, v. 18, p. 49-52, 2015.