The main purpose of this paper is to show that we can rewrite a sum of unit fractions ∑Ni = 1 1/xi< 1 in which 0<xi≤xi+ 1 to the form ∑Ni = 1 1/x′i in which 0 <x′i<x′i+ 1. In other words, it is always possible to remove duplication from ∑Ni = 1 1/xi, without changing its length. Moreover, using this rewriting process, we get a new algorithm for the expansion of Egyptian fractions. We state this algorithm and show some numerical results.
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