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## Main Question or Discussion Point

Given [tex]A_1 = 3 \texttt{ and } A_n = A_{n-1}^{2} -2[/tex]; is there a way to prove the following:

[tex]\prod_{i=1}^{n}A_{i} = F_{2^{n+1}}[/tex]

or if someone has already proven this, can you give the reference?

[tex]\prod_{i=1}^{n}A_{i} = F_{2^{n+1}}[/tex]

or if someone has already proven this, can you give the reference?