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Math Help - great probelm

  1. #1
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    great probelm

    Ok, so lets say we have these cases

    a is a real number between 1 and 2. (non-inclusive)
    b is an integer greater or equal to 2.

    Now we have a series that is like

    floor(a), floor(2a), floor(3a), floor(4a)...where it has infientlely many terms.

    Prove that the series will also contain infientely many integer powers of b. That is for any value of a and b that satisfy the cases.
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  2. #2
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    Quote Originally Posted by mathwizkid1 View Post
    Ok, so lets say we have these cases

    a is a real number between 1 and 2. (non-inclusive)
    b is an integer greater or equal to 2.

    Now we have a series that is like

    floor(a), floor(2a), floor(3a), floor(4a)...where it has infientlely many terms.

    Prove that the series will also contain infientely many integer powers of b. That is for any value of a and b that satisfy the cases.
    this is not true. i think, at least, we need to have a \notin \mathbb{Q}.
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  3. #3
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    can it skip some integer powers of b? like can b^4 be in it, but not b^5..it just has to keep on containing right?

    because i think then it might work...but why only restricted to 1 and 2? i think it would work for almost any real number a?
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