Pell and Pell-Lucas numbers of the form $-2^a-3^b+5^c$

Abstract

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Padovan and Perrin numbers of the form xᵃ ± xᵇ + 1

“…In [1], Bravo and Luca determined all the generalized Fibonacci numbers which are some powers of two. Very recently, Qu and Zeng [10] determined all the Pell and Pell-Lucas numbers that are of the form −2 𝑎 − 3 𝑏 + 5 𝑐 , where 𝑎, 𝑏 and 𝑐 are nonnegative integers with some restrictions. For more related results, one can see [3-5, 7, 12].…”

Pell and Pell–Lucas numbers of the form $$x^a\pm x^b+1$$

“…Recently, in 2017, Bravo et al [1] determined all the solutions of the equation P ' þ P m þ P n ¼ 2 a (powers of two as sums of three Pell numbers), in nonnegative integers. Very recently, Qu and Zeng [14] determined all the Pell and Pell-Lucas numbers that are of the form À2 a À 3 b þ 5 c , where a, b and c are nonnegative integers with some restrictions. Now, we are interested in studying the Pell and Pell-Lucas numbers which are in the form of x a AE x b þ 1.…”