hi, have been stuck with this one for some time, would be grateful if someone could help me out :
how do i calculate (1/105) mod(2) ?
You need to solve $\displaystyle 105x\equiv 1(\bmod 2)$ but $\displaystyle 105\equiv 1(\bmod 2)$ so $\displaystyle x\equiv 1(\bmod 2)$.
Therefore, $\displaystyle 1$ is the inverse of $\displaystyle 105$.