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Math Help - divisible by prime

  1. #1
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    divisible by prime

    Let x be a positive real number and let d be a positive integer. Prove that the number of positive integers less than or equal to x that are divisible by d is [x/d].

    I am having trouble with this one. If anyone could help that would be terrific!
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  2. #2
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    Quote Originally Posted by meshel88 View Post
    Let x be a positive real number and let d be a positive integer. Prove that the number of positive integers less than or equal to x that are divisible by d is [x/d].

    I am having trouble with this one. If anyone could help that would be terrific!

    Write \frac{x}{d}=a_0+r\,,\,\,a_0\in\mathbb{N}\,,\,\,0\l  eq r < 1 \Longrightarrow \left[\frac{x}{d}\right]=a_0
    But a_0 is the number of whole (integer) times that d "fits" into x, meaning: d, 2d, 3d,\ldots,a_0d are all multiples of d less than or equal x, and every multiple of d less than or equal x must be one of these (why?), so...

    Tonio
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