Problem Solving (PS) | For how many pair(s) of positive integers m and n, such that

You’ve to check for \( m^{(1/m)}<n^{(1/n)} \)

Take \(f(x)=x^{(1/x)}\)

The function increases and attains max at x=e (2.71).

As 1<m<n
Hence you’ve to check for x=2,3,4. For x beyond 2.71, function decreases hence the inequality won’t hold true.

So we have only 2 solutions.

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Statistics : Posted by Oppenheimer1945 • on 17 Jun 2019, 00:54 • Replies 5 • Views 4154

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