Abstract
In this article, we show that Zaremba’s conjecture holds for positive integers that appear as values of polynomials resulting from a recurrence formula and their powers of two. For example, Zaremba’s conjecture holds for all positive integers less than or equal to 100 and their powers of two. Also, as a special case, Zaremba’s conjecture holds for positive integers that appear as values of Fibonacci polynomials and powers of two.
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