On Dec 8, 2012, at 7:27 PM, Volker Braun <vbraun.n...@gmail.com> wrote:

> Solving a linear diophantine equation is an application of the Smith form.
> 
> A quadratic diophantine equation can be solved with the Hasse-Minkowski 
> theorem, though thats is definitely more advanced 
> (http://en.wikipedia.org/wiki/Hasse%E2%80%93Minkowski_theorem)
> 
> If its not one of these cases then you are pretty much out of luck ;-)

I know basically nothing about Diophantine equations, but they have come up in 
my research a few times.  Is there some sort of database of which equations 
have been solved (or not).  I'm thinking something along the lines of the OEIS 
that would allow you to search for an equation to find out what could be said 
about it.  I couldn't find any such thing on google, but it seems nearly 
inconceivable to me that such a thing wouldn't exist.  Or are number theorists 
just born knowing this stuff.  :-)

-Ivan

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