let $\{p_1,p_2,p_2,\cdots ,p_r\}$ be the set of $r$($\ge2$) pair wise distinct prime numbers
i.e.., $(i\ne j \implies p_i \ne p_j)$ for all $1\le i,j\le r$
${Statement}$ :
For any such $\{p_1,p_2,p_2,\cdots ,p_r\}$ there exists a unique set of integers $\{l,l_1,l_2,l_3,\cdots, l_r \}$, satisfying
$\dfrac{1}{p_1p_2p_3\cdots p_r}+\dfrac{l_1}{p_1}+\dfrac{l_2}{p_2}+\dfrac{l_3}{p_3}+ \cdots + \dfrac{l_r}{p_r} = l$
where $1 \le l \le r-1$ and for all $1\le i \le r$ , $1 \le l_i \le p_i-1$