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

Algebra
Mathguy442 Mathguy442
3
Report
  • Savionf Savionf
    0

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

  • Erdos Erdos
    0

    See the greedy algorithm for egyptian fractions : https://rosettacode.org/wiki/Greedy_algorithm_for_Egyptian_fractions#REXX

1 Answer

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

Mathe Mathe
3.7K
  • Erdos Erdos
    +1

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

Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.