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Note on squarefree integers through a set theoretical property


Abstract


In this paper, we show a property of set theory, that in number theory has the following consequence: if a_{1} < a_{2} < \ldots < a_{n} are squarefree integers, then the number of distinct ratios  a_{i}/(a_{i},a_{j}) is greater than or equal to n, where(a_{i},a_{j}) denotes the greatest common divisor of a_{i} and a_{j}.

DOI Code: 10.1285/i15900932v19n2p227

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