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MMO 226 Moscow MO 1952 7-digit numbers from 1, 2, 3, 4, 5, 6, 7

Source:

August 8, 2019
number theorydivisible

Problem Statement

Seven chips are numbered 1,2,3,4,5,6,71, 2, 3, 4, 5, 6, 7. Prove that none of the seven-digit numbers formed by these chips is divisible by any other of these seven-digit numbers.
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