1. ## 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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2. ## Re: Number base question

Originally Posted by flashylightsmeow
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.

3. ## Re: Number base question

Originally Posted by Plato
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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4. ## Re: Number base question

Originally Posted by flashylightsmeow
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 $n$.