3D - 2

I need to find a number d, such that 3d = 1 (mod 40)?

ok i'll be honest, i already know the answer. but how do i get to this answer? There's no point in me knowing if i don't know how to get there!! Please help!

Public Comments

1. 3d = 1 (mod 40) (3 * 27)d = 27(1) (mod 40) 81d = 27 (mod 40) d = 27 (mod 40)
2. You are looking for the inverse of 3 modulo 40. Construct this inverse as follows: 3d = 40e + 1, reduce mod 3, e + 1 = 0 mod 3, e = 2. 3d = 40*2 + 1 = 81. Solve, d = 27.