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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 6

On square Tribonacci Lucas numbers

Nurettin Irmak
Sayfa
1652–1657
Yayın Tarihi
2022-10-18
DOI
—
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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).

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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).
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Tribonacci sequence · Tribonacci Lucas sequence · squares

Abstract

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).

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Bu Makaleye Atıf Yap

Irmak, N. (2022). On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 6, 1652–1657. https://ajindex.com/articles/529528

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Kaynakça (6)

  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
  5. 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
  6. 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.