> have a common factor.
>
> The only examples I could generate in a few minutes of playing with a
> spreadsheet are 32^3 + 8^5 = 16^4, and 15^4 + 15^5 = 30^4.
>
There's a pattern there that could be exploited to generate an infinite number
of examples of a certain type -- for instance 31^5 + 31^6 = 62^6 and (working
backwards) the simpler example 7^3 + 7^4 = 14^3 . But that hardly takes us in
the direction of a solution. On the whole this problem just does not seem as
_compelling_ as FLT. But it is still of interest to note that
easily-understood conjectures that are surprisingly deep still lurk around the
corner -- everything has not yet been taken beyond everyday reach.
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
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