The statement of Sierpinski's Conjecture is 'for every integer $n>1$, there exist three integers $a,b,c$ such that $\frac{5}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$
Would this conjecture be proved if we could show this for every prime number n ?
If this is true, how do we prove this?