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On solutions of ∑ᵢ₌₁ⁿ 1/xᵢ = 1 in integers of the form 2ᵃ kᵇ

14 Feb 2024arXiv:2402.09515links table onlyarchive 2025-07-28

Joel Louwsma

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We give an algorithm that produces all solutions of the equation ∑ᵢ₌₁ⁿ 1/xᵢ = 1 in integers of the form 2ᵃ kᵇ, where k is a fixed positive integer that is not a power of 2, a is an element of {0,1,2} that can vary from term to term, and b is a nonnegative integer that can vary from term to term. We also completely characterize the pairs (k,n) for which this equation has a nontrivial solution in integers of this form.

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