PURE PRODUCT POLYNOMIALS AND THE PROUHET-TARRY-ESCOTT PROBLEM

An n-factor pure product is a polynomial which can be expressed in the form Pi(i = 1)(n) (1 - x(alpha i)) for some natural numbers alpha(1), ...,alpha(n). We define the norm of a polynomial to be the sum of the absolute values of the coefficients. It is known that every n-factor p ure product has norm at least 2n. We describe three algorithms for det ermining the least norm an n-factor pure product can have. We report r esults of our computations using one of these algorithms which include the result that every n-factor pure product has norm strictly greater than 2n if n is 7, 9, 10, or 11.