Throughout this paper e denotes an integer ⩾ 3 and p a prime $\equiv 1 (\mod e)$. With f defined by p = ef + 1 and for integers r and s satisfying $1 \leqslant s < r \leqslant e - 1$, certain binomial ...

Using a relationship derived from a special case of DeMoivre's Theorem, we can express the sine and cosine functions as infinite series of generalized binomial coefficients. We will derive these ...