Problem 13E

Find the solutions of the congruence 15 x 2 + 19 x ≡ 5 (mod 11). [Hint: Show the congruence is equivalent to the congruence 15 x2 + 19 x + 6 ≡ 0 (mod 11). Factor the left-hand side of the congruencc; show that a solution of the quadratic congruence is a solution of one of the two different linear congruences.]

Solution:

Step 1:

In this problem, we have to show that a solution of the quadratic congruence is a solution of one of the two different linear congruence.