Question

Solve/find the unique solution for x --> x + a = b (modular arithmetic) in ?n, for any n

a) x ≡ b - a (mod n)
b) x ≡ a - b (mod n)
c) x ≡ b + a (mod n)
d) x ≡ a + b (mod n)

Answer 1

To solve the modular arithmetic equation x + a ≡ b (mod n), we subtract a from both sides of the equation, yielding the unique solution x ≡ b - a (mod n).

Step-by-step explanation:

The student is asked to solve the equation x + a ≡ b (mod n) to find the unique solution for x in modular arithmetic, within the set of integers modulo n. When solving such equations, the goal is to isolate x on one side. Utilizing standard arithmetic manipulation in the context of modular arithmetic, we can subtract a from both sides to find the solution.

By subtracting a from both sides, we have x ≡ b - a (mod n), which is the correct solution. To put it another way, x is congruent to the difference of b and a, modulo n.

Therefore, the correct answer is a) x ≡ b - a (mod n).