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

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

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Conjecture re Fibonacci numbers

**Physics Forums | Science Articles, Homework Help, Discussion**