Linear combinations of prime powers in X-coordinates of Pell equations

Terms of recurrence sequences in the solution sets of generalized Pell equations

“…Lemma 3.1. Let u 0 and v 0 be the smallest positive solutions (in x and y, respectively) of the equation (7) x 2 − dy 2 = 1.…”

“…For related result, for example concerning sums or linear combinations of integers with fixed prime factors in the solution sets of Pell equations, see e.g. the papers [7,9,18] and the references there.…”

Sums of $S$-units and perfect powers in recurrence sequences

“…, solved equations of the form U n = 2 a + 3 b + 5 c completely, where U n is one of the Fibonacci, Lucas, Pell and associated Pell sequences, respectively. Also, Hajdu et al [12] and Erazo et al [6] investigated the problem of S-units in the x co-ordinate of solutions of Pell equations. For other related problems concerning S-units and recurrence sequences, one can go through ( [7,8,9]).…”