Olivet– ZAC du Larry, Zone 2

2 Instructor : Larry Guth Transcribed

2 Instructor : Larry Guth Transcribed

2 Instructor : Larry Guth Transcribed By

Question 1.2. Suppose g(k) is the least number of powers to make Theorem 1.1 hold. How big is g(k)? To provide some intuition, take n = 2−1. In its decomposition any ai can’t be greater than 1, since 2 k > 2 − 1. Therefore, ai = 1 for all i and g(k) ≥ s = 2 − 1. The real value of g(k) is only a little worse than that. Thus, the number g(k) grows at least exponentially with respect to k. However...

2 Instructor : Larry Guth Transcribed by Ruoxuan

Larry.