On square Tribonacci Lucas numbers

Abstract

The Tribonacci-Lucas sequence $\left\{S_n\right\}$ is defined by the recurrence relation $S_{n+3}=S_{n+2}+S_{n+1}+S_n$ with $S_0=3,S_1=1,S_2=3.$ In this note, we show that $1$ is the only perfect square in Tribonacci-Lucas sequence for $n\equiv ̸1\left(\mathrm{mod}32\right)$ and $n\equiv ̸17\left(\mathrm{mod}96\right).$

Keywords

• Tribonacci sequence
• Tribonacci Lucas sequence
• squares

References

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