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We prove new upper bounds on the number of representations of rational numbers m n as a sum of four unit fractions, giving five different regions, depending on the size of m in terms of n . In particular, we improve the most relevant cases, when m is small, and when m is close to n . The improvements stem from not only studying complete parametrizations of the set of solutions, but simplifying this set appropriately. Certain subsets of all parameters define the set of all solutions, up to applications of divisor functions, which has lit
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