MathDB
Atoms among 100 digit numbers

Source: Romania TST 3 2012, Problem 4

May 11, 2012
inductionvectorcombinatorics proposedcombinatorics

Problem Statement

Let SS be a set of positive integers, each of them having exactly 100100 digits in base 1010 representation. An element of SS is called atom if it is not divisible by the sum of any two (not necessarily distinct) elements of SS. If SS contains at most 1010 atoms, at most how many elements can SS have?
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