Hey everyone, I am finding these difficult and need some help solving these by hand.

1. $\displaystyle x \equiv 10^{100} \ mod \ 1001$, so I want the remainder of $\displaystyle \frac{10^{100}}{1001}$.

2. solve $\displaystyle 26^{24} \equiv 1 \ (mod \ 35)$, so I am trying to use Euler's Theorem with a=26 and n=35.

Any help would be very nice.

Thanks.