Question 3
Define $a_1=5$, $a_2=13$, and $a_{n+1}=5a_n-6a_{n-1}$ for $n\ge2$.
a) Prove that any two consecutive terms are relatively prime.
b) Prove that if $p$ is a prime divisor of $a_{2^k}$, then $2^{k+1}$ divides $p-1$, for every natural number $k$.
a) Prove that any two consecutive terms are relatively prime.
b) Prove that if $p$ is a prime divisor of $a_{2^k}$, then $2^{k+1}$ divides $p-1$, for every natural number $k$.