Hi I need help on this question:
Consider the sequence of positive integers an, for $n ≥ 1$, defined by $a_n = 6^{2^n} + 1$.
(a) Prove that the elements of this sequence are pairwise co-prime, i.e. prove that if $m$ is not $n$ then $gcd(a_m, a_n) = 1$.
(b) Show how this result, combined with the Fundamental Theorem of Arithmetic, provides another proof that there are an infinite number of primes.
Hint: Begin the first part by proving that $a_n$ $|$ $(a_{n+1} − 2)$
I've tried proving that $a_n$ is a factor of $(a_{n+1} − 2)$ but now im not sure how to carry on to prove the $gcd$ is $1$.
