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Difference in Powers of Odd Primes

  1. Dec 22, 2011 #1
    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. jcsd
  3. Dec 23, 2011 #2
    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
     
  4. Dec 24, 2011 #3
    13^3-3^7=2197-2187=10=13-3.
     
  5. Dec 30, 2011 #4
    Thanks, that saved me a lot of time trying to prove something that isn't true
     
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