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Thread: Number base question

  1. #1
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    Number base question

    Hi. I have the following problem:

    Show that 1331 is a perfect cube whatever the base b, provided that b is greater than 3.

    Now I have shown this by expanding out (b + 1)^3
    To show the coefficients as 1331.

    But this is the case for base 1 2 and 3 as well. As you get 8, 27, 64. All of which are perfect cubes.

    Could someone help me out. Thanks!


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    Re: Number base question

    Quote Originally Posted by flashylightsmeow View Post
    Hi. I have the following problem: Show that 1331 is a perfect cube whatever the base b, provided that b is greater than 3.
    Thank you for typing out the question.
    Well you have completed the task. What you fail to understand is that the digit 3 does not occur in any base less than four.
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    Re: Number base question

    Quote Originally Posted by Plato View Post
    Thank you for typing out the question.
    Well you have completed the task. What you fail to understand is that the digit 3 does not occur in any base less than four.
    Ah of course. That makes sense. Bases less than 3 wouldn't have those coefficients.


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    Re: Number base question

    Quote Originally Posted by flashylightsmeow View Post
    Ah of course. That makes sense. Bases less than 3 wouldn't have those coefficients.
    Let's all be clear. if $abcd_n$ is a number in base $n$ then each of $a,~b,~c,~d$ is a non-negative integer that is less than $n$.
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