November 24–November 30, 2009

Problem

For any function f(x), define f1(x) = f(x) and fn(x) = f(fn-1(x)) for any integer n ≥ 2. For example, f3(x) = f(f(f(x))). Is there a quadratic polynomial f(x) so that for every positive integer n the equation fn(x) = 0 has 2n distinct real roots?

Solution

here

List of solvers

Tran Thanh Nam (Tomsk polytechnic university, Russia); John M Lee (Faculty); Lloyd Sakazaki, Qiyuan Wei, Congpa You (outside).

Tran Thanh Nam wins the prize!