Math Notes - Futility Closet

Math Notes

$\displaystyle \frac{1}{6} + \frac{1}{10} + \frac{1}{14} + \frac{1}{15} + \frac{1}{21} + \frac{1}{22} + \frac{1}{26} + \frac{1}{33} + \frac{1}{34} + \frac{1}{35} + \frac{1}{38} + \frac{1}{39} + \frac{1}{46} + \frac{1}{51} + \frac{1}{55} + \frac{1}{57} + \frac{1}{58} + \frac{1}{62} + \frac{1}{65} + \frac{1}{69} + \frac{1}{77} + \frac{1}{82} + \frac{1}{85} + \frac{1}{86} + \frac{1}{87} + \frac{1}{91} + \frac{1}{93} + \frac{1}{95} + \frac{1}{115} + \frac{1}{119} + \frac{1}{123} + \frac{1}{133} + \frac{1}{155} + \frac{1}{187} + \frac{1}{203} + \frac{1}{209} + \frac{1}{215} + \frac{1}{221} + \frac{1}{247} + \frac{1}{265} + \frac{1}{287} + \frac{1}{299} + \frac{1}{319} + \frac{1}{323} + \frac{1}{391} + \frac{1}{689} + \frac{1}{731} + \frac{1}{901} = 1$

Amazingly, each of these denominators is the product of two distinct primes (discovered by A.W. Johnson in 1978).

Can a sum of such fractions produce any natural number? That’s conjectured — but so far unproven.

(Thanks, Sid.)

September 29, 2017 | Science & Math