x-Coordinates of Pell equations which are Tribonacci numbers II

The x-coordinates of Pell equations and sums of two Fibonacci numbers II

“…Returning back to (12) and (14) and using the fact that (x 1 , y 1 ) is the smallest positive solution to the Pell equation 1, we obtain…”

“…Several other related problems have been studied where x k belongs to some interesting positive integer sequences. For example, see [2,5,6,7,9,11,12,13,14,15].…”

On the $x$--coordinates of Pell equations that are products of two Lucas numbers

“…There are many other researchers who have studied related problems involving the intersection sequence {x n } n≥1 with linear recurrence sequences of interest. For example, see [4,8,7,9,12,13,14,16,17,20].…”

On the $x$--coordinates of Pell equations that are products of two Padovan numbers

“…This is sequence A000931 on the On-Line Encyclopedia of Integer Sequences (OEIS) [21]. The first few terms of this sequence are 3,4,5,7,9,12,16,21,28,37,49,65,86,114,151, . .…”