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Need help in math
Автор LilyWhite, история, 5 лет назад, По-английски

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

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5 лет назад, # |
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$$$1^5 + 2^3 = 3^2$$$ so there's also a solution for $$$(x,y,z) = (5,3,2)$$$.

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