How would you find the most amount of unique rationals summed together, in the form of 1/x, that sum to 1, However your x has to be between 2-2023?

So basically 1/2 + 1/3 + 1/6 = 1 

thats 3 rational numbers

I need to get the most amount of rational numbers that equal to 1 altogether, please let me know if any methods or anything, thanks

  • This is a challenging and very time consuming problem. A user who may want to answer it definitely deserves a bounty!

  • Erdos Erdos

    See the greedy algorithm for egyptian fractions :

1 Answer

$\sum_{i=1}^\infty \dfrac{1}{2^i} = 1$

  • Erdos Erdos

    That's a great example, even though it does not satisfy x\leq 2023.

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