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- TL;DR Summary
- Interested in finding if proofs exist or have been published on a Diophantine equation.

I know that it has been proven that for the expression x^a -y^b = 1, only has this one integer solution, where x = 3, a =2, y =2, b = 3. I am interested in knowing if there is a proof for this expression: 2x^a - y^a =1 in which there are integer solutions for x,a, and y or if no integer solutions exist except for the trivial case where x,y = 1. How would I find a proof for this if it existed?