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Is there a book, website or something else aiming to catalogue all or many of the Diophantine equations that have already been solved?

I have two tiny books by Sierpiński in which he gives some of those, but I suspect lots of kinds of equations must have been solved. (Although I really don't have much of an idea how many.) I would like to see such a catalogue to get an idea of what has been done.

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up vote 6 down vote accepted

There is the book Diophantine Equations, by Mordell. The book was published several decades ago, so it's not up-to-date, but it's the first thing I check.

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Thanks, I'll take a look at that. – user23211 Mar 23 '12 at 19:15

Another more recent book (1998) is Smart's "The Algorithmic Resolution of Diophantine Equations".

From the preface : "Despite the long and noble career of diophantine equations, there appear to be only two books solely devoted to the study of explicit methods for their solution, namely Mordell's Diophantine Equations and de Weger's Algorithms For Diophantine Equations..." (de Weger's book adds the use of LLL-algorithm to solve diophantine equations).

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The blurb for Cohen's two volume set on Number Theory says that "the central theme is the solution of Diophantine equations". I haven't yet read these books in detail, so I'm not sure how helpful these they will be.

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For many "classical" equations, Leonard E Dickson's "History of the Theory of Numbers" vol 2 is still very useful. But that was published in the 1920s, and is inevitably miles out of date for some equations (including doubtless many of those it mentions).

Some years later someone, possibly Adrian Albert, published an updated version of Dickson's work with long bibliographies a-la Dickson; but I think that mostly covered more technical aspects of algebraic number theory rather than the classsical equations of Dickson's vol 2.

I imagine a complete catalog and bibliography today, bang up to date but in the same detail as Dickson, would require dozens of volumes and would be more a WIkipedia style project than anything one could reasonably contemplate publishing in book form.

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