Four Consecutive Integers

Find four consecutive 2-digit integers
which, when raised to some single-digit power, are each equal to the
sum of their own digits. The power can be different in each case if
required. Example: 35 and 36 begin to meet the requirements because: 35^5 = 52521875, the sum of the digits being 35 (the number we started with); 36^4 = 1679616, sum digits being 36. If 37 and 38 had similar properties, we would have the sequence of four 2-digit integers as required. Sadly, they don't, but such a sequence does exist - your job is to find it! |

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Last Updated: January 14th, 2010.