We are told that there exists a k-th order homogeneous linear recurrence relation $a_n=r_1a_{n-1}+...+r_ka_{n-k}$ which has distinct roots. We need to prove that for every $a_n$ that is satisfied by this, that the sequence of squares $a_n^2$ satisfies an homogeneous linear recurrence relation with a degree that is not greater than $\frac{k(k+1)}{2}$.
I've tried a number of strategies and haven't been able to come to any conclusions, I was hoping to get a push in the right direction.
Thanks.