In this paper, we show that each non-degenerate Lucas sequence contains only finitely many terms which can be written as products of double factorials or as sums or differences of double factorials. In particular, we find all the solutions to the products of double factorials which are sums or differences of two Fibonacci numbers, and Fibonacci numbers which are sums or differences of two double factorials.
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Zhang et al. (2024) studied this question.
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