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May 19, 2015 at 0:07 comment added GH from MO @user56827: A scan and a (partial?) English translation of Ljunggren's paper is available here: mathoverflow.net/questions/206645/…
Oct 7, 2014 at 21:21 comment added Huangjun Zhu Thanks, finally I find the book and a proof there from page 110.
Aug 7, 2014 at 19:37 comment added Daniel m3 I seemed to recall it being proved in Ribenboim's book about Catalan's conjecture (published before Mihailescu solved it), and, indeed, Shorey writes that it is (on p. 111, apparently) in his MathSciNet review of the book: ams.org/mathscinet-getitem?mr=95a:11029.
Aug 7, 2014 at 19:34 comment added GH from MO @user56827: I don't know about an English translation, but there are many authors who work on this equation (e.g. see MathSciNet). These authors might know about a source (e.g. lecture notes or a book) where the proof is available in English. If I were you, I would contact the experts by email.
Aug 7, 2014 at 18:54 vote accept Huangjun Zhu
Aug 7, 2014 at 18:50 comment added Huangjun Zhu Thanks. Is there an English translation of Ljunggren's paper?
Aug 6, 2014 at 18:22 history edited GH from MO CC BY-SA 3.0
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Aug 6, 2014 at 18:15 history answered GH from MO CC BY-SA 3.0