Base Number Arithmetic

Question

I got no idea how to solve that problem. What I have done so far is I have randomly guessed numbers. I wanted to know a faster way to solve it in the future, just in case of some even more complex cases.

On this site, you should definitely show what you've done so far. This isn't wolfram. — Almentoe, Oct 04 '15 at 21:15

user236182 · Accepted Answer · 2015-10-04T21:23:58.243

1

I.e. solve $(b-1)^2=3b+1$, $\,b\in\{4,5,\ldots,9\}$ (because $3$ has to be a valid digit in base $b$).

$$\iff b^2-2b+1=3b+1\iff b^2=5b\iff b=5$$

edited Oct 04 '15 at 21:23

answered Oct 04 '15 at 21:12

user236182

13,324

ok, your edit changed you words out of latex. But I think I get the idea. You change P into b-1 right? – Houdineo Oct 04 '15 at 21:15
@Houdineo Indeed. And so the answer is $P=4,, b=5$. – user236182 Oct 04 '15 at 21:16

Base Number Arithmetic

1 Answers1