Let $a, b$ be two nonnegative real numbers and $n$ a positive integer. Prove that \[\left(1-2^{-n}\right)\left|a^{2^n}-b^{2^n}\right|\ge\sqrt{ab}\left|a^{2^n-1}-b^{2^n-1}\right|.\]
Problem
Source: Saudi Arabia BMO TST Day III Problem 3
Tags: inequalities, function, inequalities unsolved