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As -2^-4 = -4^-2 I think the HN and blog title should also include the word 'positive'

Or n=1 and m=1

The blog title says "distinct positive integer" which excludes that. The HN title is missing the word distinct for some reason.

Or n=0 and m=0

Is 0^0 equal to 0^0?

Yes.

Yes. I had to search for that qualification in the text. As far as I can tell, any integer works if n=m.

Yes, that is the article’s title. It should not have been changed. 1,1 is a solution.