Pleas help! I tried many ways!

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.