Journal of Integer Sequences, Vol. 17 (2014), Article 14.10.1

The 2-adic Order of the Tribonacci Numbers and the Equation Tn = m!


Diego Marques
Departamento de Matemàtica
Universidade de Brasília
Brasília 70910-900
Brazil

Tamás Lengyel
Occidental College
1600 Campus Road
Los Angeles, CA 90041
USA

Abstract:

Let (Tn)n ≥ 0 be the Tribonacci sequence defined by the recurrence Tn+2 = Tn+1 + Tn + Tn-1, with T0 = 0 and T1 = T2 = 1. In this paper, we characterize the 2-adic valuation of Tn and, as an application, we completely solve the Diophantine equation Tn = m!.

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(Concerned with sequences A000073 A248174.)

Received June 30 2014; revised version received October 1 2014. Published in Journal of Integer Sequences, October 3 2014.

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