Re: [math-fun] *^ commutators

A can have prime factors that B lacks. Example: A=6, B=32. Tom

I've been playing with commutators lately, and the following puzzle turned up ...

Suppose A and B are integers > 1.

When is A^B / B^A an integer? What values are possible?

Clearly A and B must have the same prime divisors, but the primes can occur to different powers. A = 45, B = 75 is a suggestive example.

Rich

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