Use Legendre Symbol to Solve a Quadratic Congruence

This video discusses how to solve a system of Cubic and Quadratic Congruences mod 71 .
The question is x^3==64 modulus 71
We factor a solution x=4 and use Synthetic Division to get (x+4)(x^2+4x+16)==0 mod 71
But eventually we need to solve x^2==59 mod 71
Then we find the solutions using the Legendre Symbol technique for Finding Quadratic Residues
#quadraticequations
#cubic
#congruency
#cubicpolynomial
#congruencemodulo
#cubicequation
#módulo1
#módulo
#modulusclasses
#legendre