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Year 2021, Volume: 50 Issue: 6, 1652 - 1657, 14.12.2021
https://doi.org/10.15672/hujms.651786

Abstract

References

  • [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.

On square Tribonacci Lucas numbers

Year 2021, Volume: 50 Issue: 6, 1652 - 1657, 14.12.2021
https://doi.org/10.15672/hujms.651786

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).

References

  • [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.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Nurettin Irmak 0000-0003-0409-4342

Publication Date December 14, 2021
Published in Issue Year 2021 Volume: 50 Issue: 6

Cite

APA Irmak, N. (2021). On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics, 50(6), 1652-1657. https://doi.org/10.15672/hujms.651786
AMA Irmak N. On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics. December 2021;50(6):1652-1657. doi:10.15672/hujms.651786
Chicago Irmak, Nurettin. “On Square Tribonacci Lucas Numbers”. Hacettepe Journal of Mathematics and Statistics 50, no. 6 (December 2021): 1652-57. https://doi.org/10.15672/hujms.651786.
EndNote Irmak N (December 1, 2021) On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics 50 6 1652–1657.
IEEE N. Irmak, “On square Tribonacci Lucas numbers”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 6, pp. 1652–1657, 2021, doi: 10.15672/hujms.651786.
ISNAD Irmak, Nurettin. “On Square Tribonacci Lucas Numbers”. Hacettepe Journal of Mathematics and Statistics 50/6 (December 2021), 1652-1657. https://doi.org/10.15672/hujms.651786.
JAMA Irmak N. On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics. 2021;50:1652–1657.
MLA Irmak, Nurettin. “On Square Tribonacci Lucas Numbers”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 6, 2021, pp. 1652-7, doi:10.15672/hujms.651786.
Vancouver Irmak N. On square Tribonacci Lucas numbers. Hacettepe Journal of Mathematics and Statistics. 2021;50(6):1652-7.