Problem with the modulus calculation

Question

I am trying to solve the following calculation, but I can't find the suitable value for B.

    6/3 (mod 6)
    A= 3
    B= ?
    M = 6
    (A * B) % M = 1
    (3 * B) % 6 =1

Somebody please guide me what is the problem with this.

Zulfi.

Answer 1

You are looking for an integer value for $B$ such that $3B=1 \mod 6$.

But if $B$ is even then $3B=0 \mod 6$ and if $B$ is odd then $3B=3 \mod 6$.

$B$ must be either even or odd. So there is no value for $B$ that satisfies $3B=1 \mod 6$.