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Math Help - gaps between square free

  1. #1
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    gaps between square free

    Show that there are arbitrarily long gaps between
    square free integers. That is,if k is any positive integer,there
    is a number N so that none of N + 1, N + 2, ..., N + k are
    square free.
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  2. #2
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    Quote Originally Posted by bigb View Post
    Show that there are arbitrarily long gaps between
    square free integers. That is,if k is any positive integer,there
    is a number N so that none of N + 1, N + 2, ..., N + k are
    square free.
    this claim is true only for k=1,2,3. because if k \geq 4, then for any N at least one of the elements in N + 1, N + 2, \cdots , N + k, will divide 4.
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