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Powers Which Differ by a Value of One

  1. Jul 25, 2013 #1
    Are there natural solutions for A and B which satisfy the equation


    where x and y are integers greater than 2?
    (I only include a greater than 2 stipulation because I can see a few obvious solutions such as 23+1=32)

    This has just sort of come to mind as I was thinking about the interesting differences in the prime composition of numbers differing by one, and then wondered if there were any powerful primes that differed by only one, or any powerful numbers whatsoever that differ by 1.
  2. jcsd
  3. Jul 25, 2013 #2


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