Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How to prove following statement :

Let's define an infinite sequence of positive integers :

$ a_i=\cos(4^{i} \cdot \arccos(4)) ; i=1,2,3......$

then for $n \geq 2 , F_n$ is prime if and only if :

$a_{2^{n-1}-1} \equiv 0 \pmod {F_n}$

For example :

$ a_1 \equiv 0 \pmod {F_2}$

$ a_3 \equiv 0 \pmod {F_3}$

$ a_7 \equiv 0 \pmod {F_4}$

share|cite|improve this question
cosine has range [-1, 1]. So, $a_i$ is between -1 and 1 always. Why are you looking at $a_i$ mod $F_n$? If it's congruent to 0, it IS 0. – Graphth Dec 18 '11 at 14:46
@Graphth,try to compute $\cos(4^1 \cdot \arccos(4))$ for example... – pedja Dec 18 '11 at 14:52

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.