Math’s ‘Oldest Problem Ever’ Gets a New Answer | Quanta Magazine
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.
Hasnain says:
“At the same time, it also leaves mathematicians with a new question to solve, this time about sets in which it’s not possible to find a sum of unit fractions that equals 1. The primes are one example — there’s no subset of primes whose reciprocals sum to 1 — but this property can also hold true for other infinite sets that are “larger,” in the sense that the sum of their reciprocals approaches infinity even more quickly than the reciprocals of the primes do. Just how quicky can those sums grow before hidden structure reemerges and some of their reciprocals inevitably add to 1?”
Posted on 2022-03-13T07:36:49+0000