Originally Posted by

**oldguynewstudent** Hi again,

From practice questions for upcoming test:

Solve the linear congruence: 4x $\displaystyle \equiv$ 5 (mod 11)

First find the inverse, 11 = (2)(4) + 3; 4 = (1)(3) + 1

so 3 = 11 + (-2)(4) and 1 = 4 - 3 = 4 - [ (1)(11) + (-2)(4)] = (-1)(11) + (3)(4)

So 4(3) $\displaystyle \equiv$ 1 (mod 11) and 4(15) $\displaystyle \equiv$ 5 (mod 11)

Therefore the solution is x = 15.

Is the above correct? Or since 15 -11 = 4 and 0 < 4 < 11, would 4 be a more correct answer?