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<p> and .</p>

<p>Since we don't know  or , we cannot compute  and . However, it is easy to compute their product.This is known as the <a href="page.php?w=Jacobi_symbol">Jacobi symbol</a>:<br/>
:</p>

<p>This also <a href="page.php?w=Jacobi_symbol">can be efficiently computed</a> using the <a href="page.php?w=law_of_quadratic_reciprocity">law of quadratic reciprocity</a> for Jacobi symbols.</p>

<p>However,  cannot in all cases tell us whether  is a quadratic residue modulo  or not!More precisely, if  then  is necessarily a quadratic non-residue</p><p>
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