Number theory - quadratic residues

yeland404
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number theory -- quadratic residues

Homework Statement



find all incongruent solutions of each quadratic congruence below.
X^2\equiv23 mod 77

Homework Equations


X^2\equiv11 mod 39


The Attempt at a Solution


it is suffices to X^2\equiv23 mod 7, andX^2\equiv23 mod 11,
then how to do next?
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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