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