Bunuel wrote:
For how many pair(s) of positive integers \(m\) and \(n\), such that \(n > m > 1\), is \(m^n\) not greater than \(n^m\)?
A. 0
B. 1
C. 2
D. 3
E. 4
Let m = 2, so n ≥ 3; we see that:
2^3 = 8 is not greater than 3^2 = 9, and 2^4 = 16 is not greater than 4^2 = 16. However, when n ≥ 5, we will have 2^n greater than n^2.
Now, let m = 3, so n ≥ 4; we see that:
3^4 = 81 is greater than 4^3 = 64. In fact, for any value n ≥ 4, we will have 3^n greater than n^3.
Since m^n is greater than n^m is already true
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