Question

Find all the square roots of x2 ≡ 53 (mod 77)

Answer 1

`x=\pm√(77n+53)`

Explanation:

We have been given an equivalence equation
`x^2\equiv 53\text{ (mod } 77)`. 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:

`x^2-53=77n`

Add 53 on both sides:

`x^2-53+53=77n+53`

`x^2=77n+53`

Take square root of both sides:

`x=\pm√(77n+53)`

Therefore, the square root for our given equation would be
`x=\pm√(77n+53)`.