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Nov 20, 2011 at 9:20 comment added Chris Wuthrich And the down-to-Earth application of it is : Given a polynomial $f$ with integer coefficients in several variables. In a finite amount of computations we can decide if $f$ has a root modulo $m$ for all $m>1$ or not. That of course is the quickest way to rule out that $f$ has an integer solution. The same works for systems of polynomial equations.
Nov 20, 2011 at 8:29 history answered Laurent Berger CC BY-SA 3.0