Question

Solve the polynomial congruence x² ≡ 1(mod3).

Answer 1

x is any integer not a multiple of 3

Explanation:

This is equivalent to ...

(x mod 3)² = 1

x mod 3 = ±1 . . . . . . taking the square root

Possible values of x mod 3 are 0, 1, 2 (≅-1), so the only value excluded is 0.

x mod 3 ≠ 0 . . . . . . for any integer x