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Power Digits (Posted on 2024-03-15)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: Some numbers but without a proof

| Comment 3 of 6 |

If you require n>1, there are only 79: those on

T. D. Noe's list, entries 10 through 88. (not to be confused with N (capital), the member number itself).

Edited on March 15, 2024, 6:18 pm

Posted by Charlie on 2024-03-15 18:16:24

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