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May 1, 2017 at 16:02 vote accept Jens Reinhold
May 1, 2017 at 1:44 history edited Julian Rosen CC BY-SA 3.0
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May 1, 2017 at 1:14 comment added Julian Rosen @GjergjiZaimi Yes, thank you. I amended the argument.
May 1, 2017 at 1:14 history edited Julian Rosen CC BY-SA 3.0
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May 1, 2017 at 0:18 comment added Gjergji Zaimi It seems to me that the S-unit equation only implies that the fraction $(a_{n+2}-a_{n+1})/(a_{n+1}-a_n)$ takes finitely many values. But this is enough for your argument to go through. One just has to rule out sequences of the form $ab^n+c$.
Apr 30, 2017 at 23:59 comment added kodlu I thought I found a computational counterexample (haven't double checked), but a proof clearly beats that!
Apr 30, 2017 at 23:39 history answered Julian Rosen CC BY-SA 3.0