# Only One Pair of Distinct Positive Integers Satisfy The Equation n^m = m^n

## A beautiful analytic proof of a number theoretic result

3 min readMar 18

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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…