Side Lengths of Equiangular Polygons (as seen by a coding theorist)

AbstractA tuple a = (a1,…,an) of positive real numbers is said to be equiangular if there is an equiangular polygon with consecutive side lengths a1,…,an. It is well known that a is equiangular if and only if the polynomial a(x) = a1 + a2x + … + an-1xn-2 + anxn-1 vanishes at . Here we dispense with complex numbers and borrow an idea from the theory of cyclic codes to prove that a is equiangular if and only if a(x) is divisible by .