I'm a huge fan of conjectures, and I'm fascinated by this new one. The Erdős-Strauss conjecture is that $\frac{4}{n} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$, where $n$ is greater than or equal to $2$ and is a natural number. Or, $\frac{4}{n}$, where $n$ is greater or equal to two and is a natural number, can be written as the sum of three unit fractions.
I know that I can eliminate all even numbers, because $\frac{4}{n}$ where $n$ is even can be written as $\frac{1}{0.5n} + \frac{1}{n} + \frac{1}{n} = \frac{2}{n} + \frac{1}{n} + \frac{1}{n} = \frac{4}{n}$. The way I test the odd numbers is I subtract the nearest unit fraction less than $\frac{4}{n}$ and see if the difference can be written as the sum of two unit fractions. But as $n$ keeps getting higher, my strategy doesn't work for long.
So, my question is, what's a better strategy?
2026-03-26 21:35:12.1774560912