On square Tribonacci Lucas numbers
The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
Keywords:
Tribonacci sequence, Tribonacci Lucas sequence squares,
___
- [1] B. U. Alfred, On square Lucas numbers, Fibonacci Quart. 2 (1), 11-12, 1964.
- [2] J. E. Cohn, Square fibonacci numbers, Fibonacci Quart. 2 (2), 109-113, 1964.
- [3] N. Irmak and M. Alp, Tribonacci numbers with indices in arithmetic progression and their sums, Miskolc Math. Notes 14 (1), 125-133, 2013.
- [4] A. Pethő, Perfect powers in second order recurrences, Topics in Classical Number Theory, Akadémiai Kiadó, Budapest, 1217-1227, 1981.
- [5] ——, Fifteen problems in number theory, Acta Univ. Sapientiae Math. 2 (1), 72-83, 2010.
- [6] N. Robbins, On Fibonacci numbers of the form $px^2$, where $p$ is prime, Fibonacci Quart. 21, 266-271, 1983.
- [7] ——, On Pell numbers of the form $Px^3$, where $P$ is prime, Fibonacci Quart. 22, 340-348, 1984.
- [8] O. Wylie, In the Fibonacci series $F_1 = 1$, $F_2 = 1$, $F_{n+1} = F_n + F_{n-1}$ the first, second and twelvth terms are squares, Amer. Math. Monthly 71, 220-222, 1964.
- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi