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A comment on Only one pair of integers satisfy the equation m^n = n^m.

Re:Only one pair of integers satisfy the equation m^n = n^m by keithmcnulty on Wednesday April 19, 2023 @09:59PM (#35635492)
For today’s interesting problem, we are looking to find all positive integer pairs n and m which satisfy the equation above, when n and m are distinct. If we play around with small n and m we can quickly see that 2⁴ = 16 = 4² , so the pair 2 and 4 are certainly one solution. Actually, it is the only solution.
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Re:Only one pair of integers satisfy the equation m^n = n^m by Computeiful on Wednesday April 19, 2023 @10:34PM (#35635680)
I noticed this interesting fact during my secondary school education. Additionally you can use this to prove that e is the point where a change in the exponent causes a larger result than a change in the base. E.g. (x+d)^y > x^(y+d) when y >= e for any real value d.
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Re:Only one pair of integers satisfy the equation m^n = n^m by OscarCunningham on Thursday April 20, 2023 @06:45AM (#35638262)
Only assuming y is also less than x.
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Re:Only one pair of integers satisfy the equation m^n = n^m by brazzy on Wednesday April 19, 2023 @10:32PM (#35635664)
1 and 2 are positive integers, are they not?
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Re:Only one pair of integers satisfy the equation m^n = n^m by bobsomers on Wednesday April 19, 2023 @10:35PM (#35635685)
1^2 = 1 * 1 = 1

2^1 = 2

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Re:Only one pair of integers satisfy the equation m^n = n^m by brazzy on Thursday April 20, 2023 @01:35AM (#35636763)
I shouldn't comment when I'm half asleep...
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Re:Only one pair of integers satisfy the equation m^n = n^m by bsder on Wednesday April 19, 2023 @10:33PM (#35635671)
1^2 != 2^1
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Re:Only one pair of integers satisfy the equation m^n = n^m by polishdude20 on Wednesday April 19, 2023 @10:44PM (#35635754)
1 and 1 are also a solution ?
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Re:Only one pair of integers satisfy the equation m^n = n^m by porphyra on Wednesday April 19, 2023 @10:49PM (#35635789)
Yeah OP updated the title of the article to include "distinct".
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Re:Only one pair of integers satisfy the equation m^n = n^m by RheingoldRiver on Wednesday April 19, 2023 @10:51PM (#35635796)
the original article says "distinct, positive." It was mis-transcribed to HN.
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Re:Only one pair of integers satisfy the equation m^n = n^m by andygeorge on Thursday April 20, 2023 @08:40AM (#35639023)
other way around - op updated title after submitting to hn
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Re:Only one pair of integers satisfy the equation m^n = n^m by cperciva on Wednesday April 19, 2023 @10:51PM (#35635798)
The problem requires that n and m are distinct integers.
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Re:Only one pair of integers satisfy the equation m^n = n^m by shusaku on Wednesday April 19, 2023 @11:57PM (#35636206)
Thanks for sharing. Are there any other posts on your blog you highly recommend?
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Re:Only one pair of integers satisfy the equation m^n = n^m by flippinburgers on Thursday April 20, 2023 @06:07AM (#35638076)
Is this why ... 42?
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