Erdős–Straus Conjecture Not But ChanHL Theorem

 It seems that to take half steps at $c$ does not resolve the problem,

$c=\cfrac{(f_o-1)(f_1+1)}{2}$ 

since $(f_o-1)$ and $(f_1+1)$ are even, $c$ is an integer.

$\bar{c}=\cfrac{2}{L}$

$L=\cfrac{2f_of_1(f_1+1)(f_o-1)}{2(f_o-1)(f_1+1)}$

and $L$ is an integer.

The total length of these steps $a$, $b$ and $c$ is $\cfrac{4}{n}$, we have,

$\cfrac{1}{K}+\cfrac{1}{J}+\cfrac{2}{L}=\cfrac{4}{n}$

where $K$, $J$ and $L$ are integer.

This will not prove Erdős–Straus Conjecture but this is now my very own ChanHL Theorem.

Thank you.