Without using the fact that 2803 is prime, Calculate $2^{1401} \pmod{2803}$
Usually I would do something like:
$1401 = 3\times467$
$\equiv(2^{467})^3 \pmod{2803}$
And try to simplify it down and use the mod to get it down to something I can punch in the calculator, but in this case $2^{467}$ does not help as it is still too large.
If I did $(2^{3})^{467}$ that also does not seem to help as I just end up with $8^{467}$ and is too large
What other techniques can I use here?