Journal of Integer Sequences, Vol. 19 (2016), Article 16.4.4

Tribonacci Numbers and the Brocard-Ramanujan Equation

Vinícius Facó and Diego Marques
Departamento de Matemática
Universidade de Brasília
Brasília 70910-900


Let (Tn)n≥0 be the Tribonacci sequence defined by the recurrence Tn+2 = Tn + Tn+1, with T0 = 0 and T1 = T2 = 1. In this short note, we prove that there are no integer solutions (u, m) to the Brocard-Ramanujan equation m! + 1 = u2 where u is a Tribonacci number.

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(Concerned with sequences A000045 A000073.)

Received December 22 2015; revised versions received March 15 2016; April 26 2016. Published in Journal of Integer Sequences, April 26 2016.

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