The Erdős discrepancy problem

The Erdős discrepancy problem, Discrete Analysis 2016:1, 27 pp. One of Erdős's most famous problems was his _discrepancy_ problem, which is the following deceptively simple question. Let \epsilon_1,\epsilon_2,\dotsbe a sequence of 1s and -1s and let mbe a positive integer. Must there exist positive integers nand dsuch that |\sum_{i=1}^n\epsilon_{id}|\geq m This would tell us that when we restrict to the arithmetic progression...