A. 578. For every integer n2 let P(n) be the product of all expressions of the form where the signs of the terms are chosen arbitrarily.
(a) Prove that P(n) is a positive integer.
(b) Prove that for all >0 there exists an n0 such that for every n>n0 the largest prime divisor of P(n) is smaller than .
Deadline expired on 11 February 2013.