/sci/ - Science & Math

[Anonymous No.2344448]

Let <span class="math">n[/spoiler] be an integer greater than <span class="math">1[/spoiler], other than <span class="math">4[/spoiler]. Let <span class="math">p[/spoiler] and <span class="math">q[/spoiler] be positive integers less than <span class="math">n[/spoiler] and relatively prime to <span class="math">n[/spoiler]. Let <span class="math">a = \frac{\cos (2\pi p /n)}{\cos (2\pi q /n)}[/spoiler]. Show that if <span class="math">a^k[/spoiler] is rational for some positive integer <span class="math">k[/spoiler], then <span class="math">a^k[/spoiler] is either <span class="math">1[/spoiler] or <span class="math">-1[/spoiler].

[Anonymous No.2344454]

[Anonymous No.2344513]

>posting questions harder than your average calculus homework problem on /sci/ and expecting anyone to figure it out

Yeah, good luck with that.

[Anonymous No.2344514]

[Anonymous No.2344523]

I would write a computer simulation for for n -> R, n =/= 4 but I don't wanna.