IMO 2011 Shortlist N1
For any integer d > 0, let f(d) be the smallest positive integer that has exactly d positive divisors (so for example we...
Category: Number Theory
Problem
For any integer d > 0, let f(d) be the smallest positive integer that has exactly d positive divisors (so for example we have f(1) = 1, f(5) = 16, and f(6) = 12). Prove that for every integer k ≥ 0 the number f(2k ) divides f(2k+1 ).