My Math Forum Primality Criterion for F_n(288)
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 February 22nd, 2012, 05:16 AM #1 Newbie   Joined: Oct 2011 Posts: 4 Thanks: 0 Primality Criterion for F_n(288) I asked this question on math.stackexchange but didn't get any definitive answer so I am posting it here : $\text{Let's define sequence}$$S_i$ $\text{as} :$ $S_i= T_{18}(S_{i-1})=2^{-1}\cdot \left(\left(S_{i-1}+\sqrt{S_{i-1}^2-1}\right)^{18}+\left(S_{i-1}-\sqrt{S_{i-1}^2-1}\right)^{18}\right)$ ,$\text{ with} :~~ S_0=8$ $\text{and define} : F_n(28=288^{2^n}+1" /> $\text{I found that} :F_2(28 \mid S_{17} , ~ F_3(28 \mid S_{37} , ~F_4(28 \mid S_{77}" /> How to prove following statement : Conjecture : $F_n(28 ;~ (n\geq 1)~~" /> $\text{is a prime iff}: ~F_n(28 \mid S_{5\cdot 2^{n}-3}" />

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