4x-2-mod-3-

Question Number 92211 by jagoll last updated on 05/May/20

4 x = 2 (\mod 3)

Commented by jagoll last updated on 05/May/20

x = 3 k - 1

x = 2, 5, 8, 11, 14, \dots

Answered by Rio Michael last updated on 07/May/20

4 x \equiv 2 (\mod 3)

here we still have one solution

since 4 and 3 are relatively prime .

4 = 1 (3) + 1

4 = 3 (1) + 0

\Rightarrow 1 = 4 - 3

1 + 3 = 4

multiplicative inverse is 1 .

1 \times 4 x \equiv 1 \times 2 (\mod 3)

x \equiv 2 (\mod 3) should be our only solution