## Digital Self Powers

The *self-power* of a number \(x\) is defined to be \(x^x\). The *digital-self-power* of a number is defined to be the sum of the self powers of all of its digits (in base 10). For example, the digital-self-power of \(402\) is \(4^4 + 0^0 + 2^2 = 256 + 1 + 4 = 261\).

Part A | Find an integer which is one more than its digital-self-power. | |
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Part B | Find an integer (greater than 1) which equals its digital-self-power | |

Part C | Find a positive integer which is one less than its digital-self-power | |

Part C | Find a positive integer which is one less than its digital-self-power | |

Part D | Find the largest integer which is at most one away from its digital-self-power |