Post ATaPbTK7TWa4xMa34S by Gusted@social.linux.pizza
 (DIR) More posts by Gusted@social.linux.pizza
 (DIR) Post #ATa3wMShz15klX9Zlg by a@social.exozy.me
       2023-03-13T18:07:22Z
       
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       #mathproblem Find all positive integers a,b,c such that a^b-b^c = (a+b)^(c-b).I found two: (2,1,1) and (7,3,5). I have no idea if there are any more.
       
 (DIR) Post #ATa47yKRXII9OOp8qW by loke@functional.cafe
       2023-03-13T18:09:26Z
       
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       @a I would love to know how to approach this problem. Perhaps someone on mathstodon will see this.
       
 (DIR) Post #ATaPbTK7TWa4xMa34S by Gusted@social.linux.pizza
       2023-03-13T22:10:06Z
       
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       @a Doesn't seem like it's possible to isolate any of the variables.This equation has no trivial simplification (other than extracting the c-b power, which helps nothing). I cannot find anything about these two tuples online (which otherwise would suggest they might be part of some sequence).FWIW bruteforcing does not yield any other solutions, for any combination of a,b,c, under 2500. Just the two you mentioned.