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On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3
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Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we find all integers [Formula: see text] admitting at least two representations as a difference between a Pell number or a Pell–Lucas number and a power of [Formula: see text]
World Scientific Pub Co Pte Ltd
Title: On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3
Description:
Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text].
In this paper, we find all integers [Formula: see text] admitting at least two representations as a difference between a Pell number or a Pell–Lucas number and a power of [Formula: see text].
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