Problem

Source: Romania TST 1995

Tags: number theory proposed, number theory



The sequence $ (x_n)$ is defined by $ x_1=1,x_2=a$ and $ x_n=(2n+1)x_{n-1}-(n^2-1)x_{n-2}$ $ \forall n \geq 3$, where $ a \in N^*$.For which value of $ a$ does the sequence have the property that $ x_i|x_j$ whenever $ i<j$.