Question

Find the integer a such that a.a ≡ 43 (mod 23) and −22 ≤ a ≤ 0.

Answer 1

Given that a is an integer from -22 to 0 such that a is equivalent to 43 (mod 23).

Such a can be obtained as follows:

a = 43 (mod 23) - 23 = 20 - 23 = -3.

Therefore, a = -3.