Suppose that $p$ is prime and $1007_p+306_p+113_p+125_p+6_p=142_p+271_p+360_p$. How many possible values of $p$ are there?

Thanks!

- **TealSeal**

TealSeal May 12, 2021

#1**+3 **

Suppose that p is prime and \(1007_p+306_p+113_p+125_p+6_p=142_p+271_p+360_p\).

How many possible values of p are there?

I don't think that there are any....

Since there are numbers up to 7 in there, the base, p, would have to be 11 or more. (because it is prime)

Looking at just the last digit.

7+6+3+5+6=27 2+1+0=3

27=3+24

This means that p must be 24 or less (not that that matters)

Anyway,

prime factors, 11 or bigger, of 24 don't exist.

So I think that there are no possible values of p that will satisfy this.

Melody May 12, 2021