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1-100 contained in union of N geometric progressions, prove N >=31

Source: Tuymaada Junior 2001 p4

April 30, 2019
geometric sequencealgebracombinatorics

Problem Statement

Natural numbers 1,2,3,..,1001, 2, 3,.., 100 are contained in the union of NN geometric progressions (not necessarily with integer denominations). Prove that N≥31N \ge 31
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