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set of 1992 positive integers and sum of elements of subsets

Source: 3-rd Hungary-Israel Binational Mathematical Competition 1992

May 24, 2007
number theory proposednumber theory

Problem Statement

A set SS consists of 19921992 positive integers among whose units digits all 1010 digits occur. Show that there is such a set SS having no nonempty subset S1S_{1} whose sum of elements is divisible by 20002000.