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Hello. I am a maths undergraduate. I am doing a project about history of mathematics. I am looking for the original solution to Hilbert's 10th problem, or at least the theorems that is accessible to my level. I have heard that Matiyasevich proof of the relationship $u=F_{2v}$ being Diophantine is accessible to undergraduate, but I can't seem to find any reference of it anywhere. The original paper is apparently not on any achieve accessible from the Internet. I look at google preview on Hilbert's Tenth Problem (by Matiyasevich) but it does not seem to contains the original proof either (though I'm trying to get my hand on a copy nonetheless). Right now all I have about the original proof is the relationship $u=F_{2v}$, and a list of relations which is the result of the original proof that can be used to construct the Diophantine equation for that relationship, all found through google. So I need help. I would like to get a reference (preferable from some place I can access easily) that contains either the original paper translated to English, or at least something that contains enough of the gist of the original proof that it can be reconstructed. Or if anyone know the original proof and if it won't take much of your time, I would appreciate it if you can just type it in as the answer too. Thank you for your help. (sorry if there is any formatting problem, because I can't find the preview button)

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The English translation was published in Soviet Math. Dokl. 11 (1970), 354–358. I don't know of an online version, but if it's not in your library you can ask a librarian how to get it by interlibrary loan. –  Henry Cohn May 14 '13 at 0:25
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There is also a book edited by Sacks about great 20th century papers in logic, where you can find the paper. Indeed, you can read it at books.google.es/books?id=9UHU_bq-wc8C&pg=PA269 –  boumol May 14 '13 at 8:19

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