Let N=d₁d₂d₃...d_n be an n-digit decimal number, with n>1.

Form the sum:
S(N) = d₁ⁿ + d₂ⁿ+ d₃ⁿ + ... + d_nⁿ

Prove that there are only a finite number of integers N for which S(N)=N.

For an extra credit, find these values of N.

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Posted by Daniel Adams on 2024-03-20 15:46:03