Link between two products

Question

Could someone help me to solve this problem :

Let's denote by $A_i$ the following product,

$$ A_i = \prod_{\substack{k=1 \\ k\neq i}}^n (a_k - a_i) $$

Is there any link or simple formula between $A_i$ and $A_j$ ?

Thank you for your answers.

Answer 1

Put $P(x)=\prod_{\substack{k=1}}^n (a_k - x) $. Then $A_i=-P’(a_i)$.