Saturday 28 February 2015

number theory - Solving quadratic equations in modular arithmetic

Is there a general way to solve quadratic equations modulo n? I know how to use Legendre and Jacobi symbols to tell me if there's a solution, but I don't know how to get a solution without resorting to guesswork. Some examples of my problems:



$x^2 = 8$ mod 2009
$x^2 + 3x + 1 = 0$ mod 13



Thanks

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