# Difference in Powers of Odd Primes

1. Dec 22, 2011

### omalleyt

I'm curious, can anyone think of a way to prove whether or not p^x - d^y = p - d, for any odd primes p,d and natural numbers x,y where x,y are not equal to one? This would be useful for a proof I am trying to work on.

So far, I have found that 3^2 - 2^3 = 3 - 2, but for this proof I am interested only in situations where p and d are both odd primes. I haven't found any examples that satisfy the equation with odd primes, but I haven't found a way to prove this equation impossible under these conditions. Ideally I would like to prove this impossible.

2. Dec 23, 2011

### checkitagain

omalleyt,

can you give more restrictive parameters?

As it is, if p = d = an odd prime, and x, y > 1, and x = y, then

p^x - d^y =

p^x - p^x =

0 =

p - d =

p - p =

0

3. Dec 24, 2011

### robert2734

13^3-3^7=2197-2187=10=13-3.

4. Dec 30, 2011

### omalleyt

Thanks, that saved me a lot of time trying to prove something that isn't true