Solve the modular equation: x^2-4=0(mod 3)

Level 1

Solve the modular equation: $x^2$ -4=0(mod 3)

3k 3k+2

1 solution

Yajat Shamji
Feb 8, 2021

$x^2 - 4 = 0 \mod 3$

$0 \mod 3 = 0$

$x^2 - 4 = 0$

$(x + 2)(x - 2) = 0$

$x = 2, -2$

From the options:

$3k, k = x, 6, -6$

$3k + 2, k = x, 8, -4$

Since $-4$ would make $x = 0$ , the answer is $3k + 2$ .

I know this is a faulty proof but this is the best I can conjure up when the problem creator is a little... clueless?

Yajat Shamji - 4 months ago