IMO 2020 Shortlist A1
Version 1. Let n be a positive integer, and set N “ 2n . Determine the smallest real number an such that, for all real x...
Category: Algebra
Problem
Version 1. Let n be a positive integer, and set N “ 2n
. Determine the smallest real
number an such that, for all real x,
N
c
x2N 1 ď anpx ´ 1q2 x.
Version 2. For every positive integer N, determine the smallest real number bN such that,
for all real x,
N
c
x2N 1 ď bNpx ´ 1q2 x.
(Ireland)