A generalization of the well–known Fibonacci sequence is the ℓ-Fibonacci sequence ${(F_m^{(\ell )})}_m$ whose first ℓ terms are $0,\dots ,0,1$ and each term afterwards is the sum of the preceding ℓ terms. The k-Pell sequence ${(P_n^{(k)})}_n$, which is a generalization of the classical Pell sequence, can be defined similarly. In this paper, we find all coincidences between these two families of sequences. That is, we find all the solutions of the Diophantine equation $P_n^{(k)}=F_m^{(\ell )}$ in positive integers $n,k,m,\ell$ with $k,\ell \ge 2$. This paper continues and extends prior results which dealt with the above problem for some particular cases of k and ℓ. In particular, it extends the previous work [2] that found all Fibonacci numbers in the Pell sequence.

众所周知的斐波纳契数列的推广是ℓ -Fibonacci序列${（F_{米}^{（\ell ）}）}_{米}$其第一个ℓ项是$0，\dots ，0，\mathrm{1个}$之后的每一项是前ℓ个项的总和。该ķ -Pell序列${（P_{ñ}^{（ķ）}）}_{ñ}$可以类似地定义是经典Pell序列的概括。在本文中，我们发现了这两个序列家族之间的所有巧合。也就是说，我们找到了Diophantine方程的所有解$P_{ñ}^{（ķ）}=F_{米}^{（\ell ）}$ 以正整数 $ñ，ķ，米，\ell$ 和 $ķ，\ell \ge \mathrm{2个}$。本文继续并且延伸其中讨论了上述问题的用于某些特定情况下先前结果ķ和ℓ。特别地，它扩展了先前的工作[2]，该工作发现了Pell序列中的所有斐波那契数。