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12
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Accepted
Egyptian fraction of a number in the interval (0.5,1)
Suppose this is known for all Egyptian fractions with minimal representation in $k$ fractions. … This allows fast enumeration of potential counterexamples: your claim for sums of 3 fractions only requires 75 sums to be tested, and for sums of 4 fractions there are 11122 sums to be tested. …