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.