Niven's Theorem #
This file proves Niven's theorem, stating that the only rational angles in degrees which
also have rational cosines, are 0, 30 degrees, and 90 degrees - up to reflection and shifts
by π. Equivalently, the only rational numbers that occur as cos(π * p / q)
are the five
values {-1, -1/2, 0, 1/2, 1}
.
@[simp]
theorem
IsIntegral.exists_int_iff_exists_rat
{α : Type u_1}
[DivisionRing α]
[CharZero α]
{x : α}
(h₁ : IsIntegral ℤ x)
: