$$5^x+7^y=z^2$$ do positive integer solutions exist, for x,y,k

Question

kainui · Answer

only solutions that can happen are when x or y is odd, they can't both be even.

dan815 · Answer

okay so what else? 
the theorem also states that x,y,k must share only 1 common prime factor?

anonymous · Answer

I can give some hints!

kainui · Answer

Oh there's probably some way to solve this problem I'm just saying using Fermat's Last Theorem.

Beal Conjecture is what I mentioned in chat... it's unproven. 

We can probably do something with quadratic reciprocity or residues or whatever though.

dan815 · Answer

thats okay i just wanted to know this bealstuff too

dan815 · Answer

to solve this i was gonna use something like the relatioship between 5 and 7s

kainui · Answer

http://norvig.com/beal.html

dan815 · Answer

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