We have a sequence $g_0=3$ and $g_n=2+g_0g_1g_2...g_{n-1}$ for $n\in \mathbb{N}$. How can I prove that $\gcd(g_k,g_n)=1$ if $k<n$? I know that this essentially asking to prove that they are relatively prime, but I am unsure where to begin. Could I show that all of the numbers in this sequence are relatively prime?
2026-04-07 12:36:40.1775565400
Proving relatively prime in a sequence?
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