perplexus.info :: Just Math : Greatest Root Power

Greatest Root Power (Posted on 2011-01-12)

Determine all possible pair(s) (M, N) of positive integers such that:

N^[√N] = M^M-1

Prove that these are the only possible pair(s) that exist.

Note: [x] denotes the greatest integer ≤ x.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(M, N)= (1,1), (2,2), (4,8) are the required solutions.
For an explanation, refer to the solution submitted by Charlie in this location.

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

	Subject	Author	Date
	computer exploration--no proof (spoiler)	Charlie	2011-01-12 13:09:55

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