IT-CESENATICO 2006 Problem 5

Consider the inequality $$(a_1+a_2+\dots+a_n)^2\ge 4(a_1a_2+a_2a_3+\cdots+a_na_1).$$ a) Find all $n\ge 3$ such that the inequality is true for positive reals. b) Find all $n\ge 3$ such that the inequality is true for reals.