A Nontrivial Diophantine Solutions

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Summary
Existence of non-trivial positive integer solutions.
Given the diophantine equation: 2x^5 - y^3 = 1 Is there any way I can prove that the only positive integer solution for this equation is: x =1, y = 1?
 

fresh_42

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Why do you ask and what have you tried so far?

We could write ##2x^5=(y+1)(y^2-y+1)## and then we get ##2\,|\,(y+1)## because ##y^2-y+1## is odd.
 
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Sorry, I don't know what you mean by the notation 2|(y+1)?
 
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It means '2 is a factor of (y + 1)'. I'm not sure if @fresh42 meant to say anything more?
 

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