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Erdős–Straus conjecture
Conjecture
For all , there exist positive integers
,
,
such that
.
See Erdős–Straus conjecture for more details.
Bibliography
* indicates original appearance(s) of problem.
Solution
On July 14th, 2014 Anonymous says:
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
On July 14th, 2013 cpbm says:
I think you need to specify that ,
and
be positive for this to be challenging (and open).
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:
![$$z=L$$](/files/tex/503d60d4e432867df52530b820e9e784b4088769.png)