What is the $10^5\pmod{35}$? How to evaluate $10^5 \pmod {35}$ ?
I tried this $a=(10^2\cdot 10^3)\pmod{35}$
then again a mod $35$.  This is very lengthy please tell me a shorter way?

$$
10^2 \equiv 30 \left[35\right] \Rightarrow 10^3 \equiv 300 \left[35\right]\equiv 20 \left[35\right]
$$
So
$$
10^4 \equiv 200 \left[35\right] \equiv 25 \left[35\right] \Rightarrow 10^5 \equiv 250 \left[35\right]
$$
So

$$
10^5 \equiv 5 \left[35\right]
$$
  ( and in fact $ 10^5=2857*35 +5$ )

