Question

Find the solution of x^2≡ 3 mod 11

(a) x ≡ -9 mod 11 and  x≡ 9 mod 11

(b) x ≡ 9 mod 11

(c) No Solution

(d) x ≡ 5 mod 11 and x ≡ 6 mod 11

I got this question in final exam.

The origin of the question is Number Theory in division More Number Theory of Cryptograph & Network Security

Answer 1

Right choice is (d) x ≡ 5 mod 11 and x ≡ 6 mod 11

Easiest explanation: On finding the quadratic congruencies we get x ≡ 5 mod 11 and x ≡ -5 mod 11.