# Erdős–Straus conjecture

 Importance: Medium ✭✭
 Author(s): Erdos, Paul Straus, Ernst G.
 Subject: Number Theory
 Keywords: Egyptian fraction
 Posted by: ACW on: February 29th, 2012
Conjecture

For all , there exist positive integers , , such that .

See Erdős–Straus conjecture for more details.

## Bibliography

* indicates original appearance(s) of problem.

### Formula Individa

It was necessary to write the solution in a more General form: - integers. Decomposing on the factors as follows: The solutions have the form: Decomposing on the factors as follows: The solutions have the form:

### Solution

For the equation: The solution can be written using the factorization, as follows. Then the solutions have the form: I usually choose the number such that the difference: was equal to: Although your desire you can choose other. You can write a little differently. If unfold like this: The solutions have the form:

### Further restriction

I think you need to specify that , and be positive for this to be challenging (and open).

Done. Thank you.