A simple fraction question that has resisted proof since 1948
Can every fraction of the form 4/n, where n is a whole number of 2 or more, always be rewritten as the sum of exactly three unit fractions (fractions with 1 on top)? For example, 4/5 = 1/2 + 1/4 + 1/20.
Reveal the answer
Nobody knows for certain. Computers have verified the Erdős-Straus conjecture for every n up into the quintillions without finding a single exception, but no one has proved it holds for all n, nor found a counterexample. Paul Erdős and Ernst Straus first posed it in 1948, and it remains one of the more approachable-sounding open problems in number theory.
— Paul Erdős and Ernst G. Straus, Erdős-Straus conjecture — 1948