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If $(3p_n\pm \sqrt{5p_n^2-4})\Delta/(2p_n)$ is an integer then $p_n$ is an odd-indexed Fibonacci number
number-theory
elementary-number-theory
fibonacci-numbers
lucas-numbers
Primality test for numbers of the form $(10^p-1)/9$ (and maybe $((10 \cdot 2^n)^p-1)/(10 \cdot 2^n-1)$)
prime-numbers
examples-counterexamples
primality-test
lucas-numbers
lucas-lehmer-test
Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$.
limits
fibonacci-numbers
continued-fractions
experimental-mathematics
lucas-numbers
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