Analytic solutions of polynomial-like iterative functional equations with variable coefficients are discussed in the complex field ℂ by reducing to an auxiliary equation and by applying known results for systems of nonlinear functional equations of finite orders.
Our goal is to study Pascal-Sierpinski gaskets, which are certain fractal sets defined in terms of divisibility of entries in Pascal's triangle. The principal tool is a carry rule for the addition of the base-q representation of coordinates of points in the unit square. In the case that q = p is prime, we connect the carry rule to the power of p appearing in the prime factorization of binomial coefficients. We use the carry rule to define a family of fractal subsets Bqr of the unit square, and we...