perplexus.info :: Numbers : Powering up the digits II

Powering up the digits II (Posted on 2009-10-22)

Each of X₁, X₂ and X₃ represents a nonzero digit of the 3-digit base M positive integer X₁X₂X₃; where X₁, X₂ and X₃ are not necessarily distinct.

Determine the respective minimum and maximum positive integer value of M, with M < 100, such that this equation has at least one valid solution.

X₁^X₁ + X₂^X₂ + X₃^X₃ = X₁X₂X₃ - 1

Note: X₁X₂X₃ denotes the concatenation of the three digits.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There exists only one solution to the given equation, which is as follows:
4 3 2 3 59 base representation decimal value
As a check:
3^3 + 2^2 + 3^3 = 59 - 1 (decimal representation)

For a detailed explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
computer solution	Charlie	2009-10-22 18:00:31
No Subject	Ady TZIDON	2009-10-22 15:39:24
No Subject	Ady TZIDON	2009-10-22 15:37:45

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