Need help in math

Revision en1, by LilyWhite, 2019-08-16 08:43:19

Suppose we have an indefinite equation about $$$x,y,z$$$.

$$$a^x+b^y=c^z$$$

If $$$(x,y,z)=(2,2,2)$$$ satisfies the equation, is there other such $$$(x,y,z)$$$ groups with $$$x,y,z \geq 2$$$ satisfy the equation?

Notice, that unlike Fermat's last theorem, $$$x,y,z$$$ does NOT have to be pairwise equal.

I think that the answer is NO, but I am unable to prove it or construct such groups. Please help me :D

Tags #math, #number theory, equations

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en1 English LilyWhite 2019-08-16 08:43:19 412 Initial revision (published)