Question 28
(GBR 5) Let us define $u_0=0,u_1=1$ and for $n\ge0$, $u_{n+2}=au_{n+1}+bu_n$, $a$ and $b$ being positive integers. Express $u_n$ as a polynomial in $a$ and $b$. Prove the result. Given that $b$ is prime, prove that $b$ divides $a(u_b-1)$.