Quadratic Congruence Equations

mathematics

$x^2 \equiv a\pmod{p}$

We've paved the way to solve $x^2 \equiv 1\pmod{p}$,which implies ${(\sqrt{a}x)}^2 \equiv a\pmod{p}$

• If $a$ is a square,then the equation will have 2 solutions.Otherwise,it has no solution.
• The sum of solutions equals p.
  

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First proof

-TBC-