# how do you bound exponent of x^2+1=y^p

for p a prime exponent using linear forms in logs?

So far I have (x-i)(x+i)=y^p which are coprime and hence x+i=(a+ib)^p , now how do I get a linear form in logs so that I can find an upper bound on p?

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– Will Jagy Jun 15 '12 at 19:43
not what link is supposed to mean, I'm not asking for a full proof of cataln's conjecture but consider this particular e.g. – Kale Jun 15 '12 at 20:34
perhaps you can give some references that use the techniques you want to apply. – Will Jagy Jun 15 '12 at 23:53
You can look up the work of Tijdeman for this kind of argument. But why would you not want to use a known theorem? – Felipe Voloch Jun 16 '12 at 0:05