>> **Question:** Are the properties as follows holds?

Let $P$ be a positive integers. We written: $P=$ $a_1^{x_1}a_2^{x_2}...a_n^{x_n}$ $=b_1^{y_1}b_2^{y_2}...b_k^{y_k}$  where $a_i, b_j$ are integers greater than $1$.

if $\Pi a_i \le \Pi b_j $ then

$$\Pi_{i=1}^n (1-\frac{1}{a_i}) \le \Pi_{j=1}^k (1-\frac{1}{b_j}) $$

$$\Pi_{i=1}^n (1-\frac{1}{a_i})^{x_i} \le \Pi_{j=1}^k (1-\frac{1}{b_j})^{y_j} $$