How to find perfect squares such that their base 9 representation is all 1s?
I am working on solving all of the problems in from the Macalester College Problems of the Week that are available in this archive, and am currently working on MacPOW 1114:
Squares of 1
Find all perfect squares whose base 9 representation consists of only 1s.
Here is my current progress on this:
- First of all, we can see that 1 is the only trivial solution - there of course have to be other non-trivial solutions.
So really our problem here is finding square numbers of the form
1 answer
The following users marked this post as Works for me:
User | Comment | Date |
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CrSb0001 | (no comment) | May 7, 2024 at 13:45 |
First I plug in
Before we prove this we should recall the geometric series formula
This means we are solving the equation
Notice that
We compute
Looking mod
We can rearrange the second equation to get
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