Question

Find all the square roots of x^2 ≡ 53 (mod 77) by hand. This is my second post. Please explain all the steps how you did this?

Answer 1

Explanation:

Given that

`x^2 ≡ 53 (mod 77)`

Right side has values as

53, 53+77, 53+2(77),+....

We have to find one which is a perfect square.

We have from this series 361 is 19 square

Thus
`x =19.`

Next is
`x^2=900\\x=30`

`x^2=2209\\x=47` and so on.