2019 U.S.A. Mathematical Olympiad Solutions
www.maa.org › usamo › 20192019 USAMO { Solutions 4 Picking n > max0 r d l P d s=r ask s r r , we conclude as above that Pd s=r ask s r r 2K. Since k was arbitrary, we can replace k by 10pk and so also obtain Pd s=r as10 (s r)pks r s r 2K for any k 2K and p 1. Fixing k and choosing p large enough yields the result, by the same argument. Suppose now that d 2.