Open Problem Garden - Erdős–Straus conjecture - Comments

Formula Individa (re: Erdős–Straus conjecture)

Anonymous — Mon, 14 Jul 2014 17:39:25 +0200

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 (re: Erdős–Straus conjecture)

Anonymous — Mon, 14 Jul 2014 17:36:44 +0200

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:

Restriction (re: Erdős–Straus conjecture)

ACW — Mon, 15 Jul 2013 18:45:49 +0200

Done. Thank you.

Further restriction (re: Erdős–Straus conjecture)

cpbm — Sun, 14 Jul 2013 23:38:49 +0200

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

Erdős–Straus conjecture

ACW — Tue, 28 Feb 2012 23:37:15 +0100

Author(s): Erdos; Straus

Subject: Number Theory

Conjecture

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