It is x2 Thank you Determine whether the following quadratic

It is x^2. Thank you!

Determine whether the following quadratic congruences are solvable: (a) x2 = 219 (mod 419).

Solution

(219/419) = (3/419)(73/419)

               = (1)(419/3)×(419/73)

               = (1)(2/3)(54/73)

               = (1)(1)(2/73)(27/73)

               = 1×1×(9/73)(3/73)

               = (3/73)

               = (73/3)

               = (1/3)

               = 1.

So the congruencex2219 (mod 419) has a solution.