Suppose that today is tuesday. what day of the week will it be in $3^{100000} + 3^{10000} + 3^{1000}$ days? Suppose that today is tuesday. what day of the week will it be in   $3^{100000} + 3^{10000} + 3^{1000}$ days ?
I figured that, eventually, I will add $3^{100000} + 3^{10000} + 3^{1000}$ and $\mod\ 7$ that answer...
I tryed with the Fermat little theorem but cant quit figure how to apply it here.
$m = n(\mod p-1)$
then , $a^m = a^n (\mod p)$
doing that I realised that $3^{x} \mod 7 = 4$ for all $x \mod 10 = 0$
when I try to apply Fermat, I end up with :
$m = 100000 \mod 6 = 4 \\ 3^4 = 3^{100000} \mod 7 $
which make no sense... 
Am I using the right theorem for the problem ? If so, how do I apply it...
Thanks

$3^6 = 1 \mod 7$. Hence $3^k \mod 7 = 3^{k-6n} \mod 7$.
$100000 = 6\cdot 16666 + 4$. $10000 = 6\cdot 1666 + 4$. $1000 = 6\cdot 166 + 4$. Hence $3^{100000} + 3^{10000} + 3^{1000} \mod 7 = 4+4+4 \mod 7 = 5 \mod 7$.
Hence it will be Sunday.
