Answer:
[tex]x=\pm\sqrt{77n+53}[/tex]
Step-by-step explanation:
We have been given an equivalence equation [tex]x^2\equiv 53\text{ (mod } 77)[/tex]. We are asked to find all the square root of the given equivalence equation.
Upon converting our given equivalence equation into an equation, we will get:
[tex]x^2-53=77n[/tex]
Add 53 on both sides:
[tex]x^2-53+53=77n+53[/tex]
[tex]x^2=77n+53[/tex]
Take square root of both sides:
[tex]x=\pm\sqrt{77n+53}[/tex]
Therefore, the square root for our given equation would be [tex]x=\pm\sqrt{77n+53}[/tex].
