Erdős Problems

Tags Prizes

OPEN

Are there infinitely many solutions to \[\frac{1}{p_1}+\cdots+\frac{1}{p_k}=1-\frac{1}{m},\] where $m\geq 2$ is an integer and $p_1<\cdots<p_k$ are distinct primes?

#313: [ErGr80]

number theory, unit fractions

For example, \[\frac{1}{2}+\frac{1}{3}=1-\frac{1}{6}.\]