Solution Found!
Find the solutions of the congruence 15 x 2 + 19 x ? 5
Chapter 4, Problem 13E(choose chapter or problem)
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.]
Questions & Answers
QUESTION:
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.]
ANSWER:
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.